As for recommendations: Pathfinder 2e* if you want extremely rigid (overly so, IMO) forced balance. Every character is within a very narrow mathematical range of every other. Most decisions are just flavor decisions. There's a lot of good in the system, but I am personally of the opinion that RPG decisions, for crunchy mechanical RPGs anyway, should have impact and not just be flavor decisions. It also is gonzo/wonky/over-the-top anything-goes anime style nuts, like "swim up waterfalls" and "jump on clouds" and "shoot while jumping to jump higher" crazy.
PF1e* if you truly want the best crunchy/mechanical experience you probably could ever hope for. Highly customizable if any of the myriad options don't work for you (including 3rd party content or backporting from D&D 3e).
13th Age* is the love child of the designers of D&D 3e and D&D 4e, and it feels like it. A 2nd edition is currently in development, but is expected to be backwards compatible as much as it can be. The system is good for a romp, and the enemies get flavorful neat powers. It's a bit open-ended loosy-goosy outside of combat though.
For
5e players, PF2 or 13th Age is going to be your easiest conversion... Though don't ignore considering going all the way to to PF1. As a note, all of PF1's core books (that were originally hardcover) are still in print as scaled-down softcover ("pocket editions"), so it's still very much available even physically.
If you want to go outside of "crunchy fantasy RPGs": Fate* is a spectacular narrative-first RPG system. It's crunchy enough still to be a game though. It's all about the players setting "dials" with adding/subtracting customized subsystems to their content. The three default flavors, Core, Accelerated, Condensed -- I prefer Core. Accelerated is best for one-shots or
short arcs. Condensed is, to me, and unnecessary simplification of Core. The Golden and Silver rules, along with Bronze "
Fate fractcal" ("anything can be a character") also makes it good for a wide variety of types of play.
Band of Blades* or
Blades in the Dark* are great for a hybrid (but mostly narrative) game designed around a campaign with a cast of characters and the group "building something" outside of just each individual character. It uses a highly-customized version of
Powered by the Apocalypse*, but changed enough I like it. (I tend not to like PBTA games.)
I, sadly, have too much of a life that there are others I haven't tried to say I recommend or not (tops being
Chaosium BRP*,
Cipher System* and
Savage Worlds [though that may be soon]). I have plenty of other good games I can recommend for niches, but not in a general RPGs post. If someone wants to hear them, let me know.
But if you've never played any RPGs and want to try a single one-shot game... my favorite overall introduction product is the mini-adventure from the (
Unisystem) All Flesh Must be Eaten
demo kit. Don't let the players know or see what it is in advance, lest it ruin the surprise!
*=System is open.