The Survive This! Games are pretty good. What Shadows Hide is the urban fantasy book, but you can get a similar effect by mixing some of those games together for a higher power level. Survive This! Zombies has modern weapons and Survive This! Fantasy has magic and monsters
BESM is a similar concept to GURPS, but on an anime scale. Crazy powers are pretty much expected, so magic users are more doable than GURPS. It's also not too hard to make a powerful character that's not a magic user. It's also not too heavy on rules
Dark Streets and Darker Secrets is great for a grittier, more dangerous game. Players need to be pretty careful, but it definitely does dark urban fantasy reasonably well
I like point crawls for this. I mark a few points of interest and how long it takes to get there. Travel is fairly abstract until they get to a point of interest. Once they get to the point of interest, things slow down so that they can find cool things, meet npcs, fight monsters or some combination of those things
If the area is hard to navigate then a failed survival check might send them to a different point of interest
I try to keep house rules to a minimum. My biggest one is a change to inspiration. Inspiration is a reroll and you need to keep the new result. You can have multiple inspirations (max 3) and you start each session with one for free. If you end the session with more than one, then you can take one extra inspiration with you to the next session
To start with you'll want either the basic rules or Player's Handbook. The basic rules are free on DnD Beyond (that's the easiest place to find them, but you can also just Google it). Personally, I say that if you're doing 5e, you should have the PHB or some way to access the player options in there
You'll want to go through the character creation section, skill checks, combat and spellcasting. That should be enough to start. Next, I highly recommend making a character. By making a character you'll learn well enough to teach your players.
And finally, nothing has been more useful to me than Matt Colville's running the game playlist. You only need the first few videos to get started, the rest is optional advice and things he likes to do
Fair, but there hasn't been a decent reboot of anything in forever.
So I'm going in with no expectations to avoid disappointment. If it's good I'll be happy, if it's bad I won't be surprised