The physical books can be had on secondhand bookstores for significantly less, albeit they're still sold for more than they aught to be, usually. Thriftbooks is an online reseller that has them for around $25 USD but local thrift stores and library book sales have them sometimes and will sell them for next to nothing.
There are some inexpensive/free programs/websites that exist to automate and simplify basically everything in the game. IME the only advantages the manuals have over the apps is that the manuals convey the bigger picture of how the game works.
Pick a different system, or download copies and have them printed, or just print the key pages, or look for used copies. Also 5e.tools is a great resource
Do not let WotC trick you into thinking you need to pay them 150 bucks to start a game.
One, sail the high seas if you really wanna play D&D 5th edition (or whatever new edition they come out with).
Secondly, consider other systems. Depending on what exactly you wanna get from D&D (solving problems in a fantasy setting, character customization, playing in a particular setting, character drama in a fantasy setting, battles with cool powers, a sense of progressing from a nobody to a hero, feeling like a hero from day 1, etc) there is probably a better system for that than 5e and the majority of them don't require more than 2, or often even just 1 book. Plus several that have 2 only charge for digital versions of the GM book.
Oh, consider dungeon world. It's a simpler system that lends itself to fail forward, and the basic moves/character sheets are all available for download for free.
Looking at this now. The mechanics look simpler for sure. I’m playing a game just me and my wife and she’s never played a tabletop rpg before, so that might be a good call.
Oh if you've got a new person then fuck d&d unless they really want to specifically play d&d. If not, there are way better systems for shared storytelling. I introduce people to rpging via dungeon world 10 times out of 10.
Monster of the Week? Anything Powered by the Apocalypse is going to be much stronger in Game Master support and explanations than D&D. If you want something friendlier there are also games like Yazeba's Bed and Breakfast that has no focus on combat. Wanderhome, as well -- albeit that one isn't modern. You've got a lot of options, don't be fooled by Hasbro!
As others have said, pirate things. I'd also suggest looking for legally dubious online resources, lots of websites out there that have SRDs and splatbooks laid out in an easier-to-navigate website ways than PDFs.
Though, I am going to be that guy and tell you that Pathfinder 2e has most of its rules online at this website and it's much better in terms of balance and not being racist
Dungeons and Dragons is like a specific name-brand RPG product owned by a shitty company called Wizards of the Coast.
Other people and companies make other RPG systems. Pathfinder is probably the biggest and is pretty similar to DnD and has a similar setting. However there's so many games and settings that you can really find something for anyone. Like giant robots? Magical girls? 80s "kids on bikes" adventures? Post apocalypse wastelands? Vampires and werewolves? Etc - there's probably a game that would suit your group
Advising Pathfinder is a terrible for new player. Heck, i played and GM'ed dozens of different systems over 30 years and Pathfinder has been one of the most miserable and abysmal experiences for me.
Yeah, generally they're playing another D&D-style game, or more rarely a game that's an entirely different genre. Game like Pathfinder (2e is the big internet favorite atm) and OSR games are designed to be basically the same niche genre of "dungeon-crawling, combat-centric high fantasy" but with different rules. Other games like Dungeon World use the same setting concept but the rules are more narrative-focused with less emphasis on hours-long combats on a grid. Further afield are generic systems like FATE, GURPS, Savage Worlds, etc which are flexible and can be used to play whatever genre you want, so they can be D&D-fantasy or cyberpunk, superheroes, historical fantasy, "action movies", etc (though most of these tend to be best at one or a few things). Or you can just play something totally different like Lancer, a game set in the space communist future where you fight slavers and fascist remnants in giant mechs, or Thirsty Sword Lesbians, which I know very little about except that the name is funny and that it is very queer.
Personally I use GURPS, because it does a lot of things I like and because it can be used to run different genres with minimal effort. Things like extreme customizability, crunchy combat that actually has multiple options worth choosing that aren't just 'spam attacks', no HP bloat, point-buy characters with no classes (unless you want them), I could go on.
I loved GURPS. My brother and I played all the time. Also want to shout out Kevin Crawford's Stars without Number if you're looking for a scifi game. He has a free to download basic version, which is fully playable, and a paid version which has some optional rules and tools..
I prefer Basic fantasy for fantasy gaming but Worlds Without Number is also a great option (again free and premium versions)..
D&D kind of sucks, and especially sucks for what you want to do.
It's not good for 1:1 games. It makes many assumptions about there being a full party
It doesn't offer much advice for DMing, and has a lot of ways to fuck it up.
It has like no rules for roleplay. It has very vague "If you roll a high number maybe they'll do you a favor" suggestions, but for something like "I want to stand up straight, look him in the eye, and tell him he should yield or suffer the wrath of my patron" it leaves it entirely up to the DM how to resolve. Other games provide a lot more guidance
It is entirely combat focused. It is crunchy in annoying ways.
Chronicles of Darkness is modern day occult. it's not very light, but it's closer to what you want. I'm fond of Mage: The Awakening.
Fate is a good general purpose system that's more in line with how I think people imagine RPGs are. It's also free. It cares a lot more about the narrative than D&D. D&D puts most narrative detail squarely in "unimportant flavor". So if your character's story is they were a pirate, that doesn't do anything in the game unless you have the pirate background, and those tend to be very limited. Contrast with Fate that is much more explicit about "Aspects give you permission. If your character has 'Former Pirate' on their sheet, they definitely know some sea shanties and how to move around on a boat". D&D leaves that up to the DM. And then a lot of people are like, if it's leaving so much up to the DM why am I even buying this book.
Powered by the Apocalypse games are also popular. I don't personally like them that much, but I see why people do.
They don't. One of the many, many things that sucks about D&D is that it's the most recognised, so people think it's a good place to start with TTRPGs.
It's not. It has most of the complexity of a crunchy game like PF2e, but no mechanical unification, so every action has its own rule, rather than similar actions just being small variants on the same. Rules are often specific, applying only to certain situations, but still vague, forcing the DM to decide how they're actually meant to be applied. Similarly, it's very crunchy and combat focused but combat is pretty barebones, just being a case of standing in front of an enemy and hitting it until one of you falls over. Could be either you or the enemy, the balance is skewed at best.
As if there weren't enough mechanical problems, the lore stagnated after 3.x, and wasn't that deep even then; The Forgotten Realms setting in particular is extremely barebones once you're off the Sword Coast, and regularly leans all the way over to downright offensive. Like ye olde minstral show racism in stuff printed in the last 5 years. And they charge you a fucking arm and a leg for everything, so, like you say, you need to pay like $150 just to play in a homebrew setting.
You don't want to play D&D. If you do, you want to play Pathfinder 2e, Savage Worlds, or Shadow of the Demon Lord/Weird Wizard instead. Pathfinder in particular has great fey lore, even if you pick a different system it'd be worth looking at Kingmaker for fey storyline ideas.
What you probably want is something like Fate or Monster of the Week, a more storytelling focused system that isn't so balanced around parties. FitD games would also be worth looking at.
Regarding Edit 2, when you say more modern do you mean like urban fantasy?
I'm a big fan of the Chronicles of Darkness games (which, fair warning, new books aren't coming out, but you can get a PDF or print on demand copy of any of them, and like most non DND games you're looking at 1 core book only).
I really like Werewolf the Forsaken but it's pretty focused on playing a pack of werewolves. If she's into faeries you could look at Changeling the Lost (which may or may not be suitable, it's about humans who've escaped captivity after being captured by the "True Fae." They're changed by the experience and couldn't fit back into their old lives even if there weren't a doppelganger made of garbage and fae magic living their life, and they may have conflicting feelings about the whole thing anyway, after all if they hadn't gotten kidnapped they wouldn't have learned to magically learn someone's greatest desire or talk to birds or whatever. Worth pointing out that it's a horror game and the fae world kind of represent trauma).
If that one doesn't spark joy, Vampire the Requiem is also really cool and is about trying to survive as a relatively new vampire in a cutthroat, backward citywide society of the undead. It's not about violence in the sense of combat but vampires are obviously predatory so this could also maybe not be right.
The same line of games has one about being a wizard in the modern day, but it's extremely heavy and crunchy and probably not what you're looking for.
If you mean you're interested in non-fantasy modern settings I don't know much about the available games but I'm sure there are some decent ones someone else will mention.
5e tools, that'll help you with mechanics and items. If you want the books, DM me and I'll throw you a link to my drive where I got some of em stored, including the newest phb.
Though, you said she wanted something more modern. Maybe try CBR + PNK? The gist of it is, it's the character's last job. The character sheet fits on a pamphlet. If you want something a bit more detailed but still with ample room for mechanics, I'm reading through Savage Worlds and it looks superior to 5e in regards of speed of combat and roleplayability. Plus, there's loads of third party content to make the system fit pretty much any setting, including weird west (Deadlands), cyberpunk (there's a bunch of them), superheroes (i think it was called Capes, but I might be wrong), to fantasy (Paizo made a Pathfinder port to Savage Worlds).
As someone who just recently (1yr) started DM'ing, go for something simple. Don't drown yourself in options. And try not to homebrew too much. Go for a one-shot, but feel free to stretch it out to two or three sessions. You need any help, my DM's are open. 5e isn't as simple as some people say due to mistakes done by WotC and you need some elbow grease to buff it out as a DM.