[L.J.Steele]

I'm pondering these factors:

Name Recognition
Easy of Play, particularly to start
Size/Cost /Availability of Books and on-line support
Introduction to different styles and genres

It might also make sense to recruit some local GMs for a couple of demo days, running short adventures in the chosen systems for anyone who signs up or wanders in.

First: D5e -- you have to cover D&D in some form. D5 is reasonably newbie friendly. Pair it with a least one of the adventure books for folks who don't want to start with bespoke adventures.

Second: Fate Core or Fate Accelerated -- introduction to the indie game player-centered, collaborative style. Can use d6s instead of specialized fate-dice. Pair it with any of the Fate world books or world collections to help get a game off the ground. If Dresden Files is popular at your library, Dresden Files Accelerated is a good choice.

Third: I'm leaning towards an incarnation of CoC -- Pulp Cthulu or Trail might be good places to start. Again, pair it with a decent adventure. As other have said, it's venerable for good reasons and offers a very different game style and experience.

If West End Star Wars were still in print I might go there for the third, just for the ability to tie game to pop culture easily. Don't know the current Star Wars RPG well enough to comment on it.

Others:

I like Hero. I've played incarnations of it since the original Champions. But, the most recent edition I have is a doorstop of a tome with long, complex rules section to tune a character to what you want. It's a great system, but I'd call it an intermediate one, not an intro one.

I like GURPS, obviously. Again, played incarnations going back quite a ways. But again, a pair of hefty books just to get started. Again, lots of options and the ability to tune characters at a fine level, but an intermediate system, not an intro one. If Discworld is popular in that library, maybe GURPS Discworld with the GURPS Lite system.

A few other ideas:

13th Age -- I hear good things of it as a variation on the d20 fantasy game.

Bubblegumshoe -- variation on Gumshoe for teen investigators. Heavy on social combat, light on actual fighting. Won the Ennie for Best Family Game last year.

Cthulhu Confidential -- a 1 GM/1 Player variant of Gumshoe, good for folks who don't have an established body of players.

Dracula Dossier -- spies meet vampires. It won a bucket-load of awards in 2016.

Feng Shui -- written for fast, action heavy play. A good way to draw folks in.

Mouse Guard -- haven't played it, but hear good things of it. I think it ties in nicely to the Redwall books.

Paranoia -- haven't read the latest edition, but older ones were lots of fun to read, tho needed the right GM to play.

Pathfinder -- haven't played it myself, but it's been popular in local circles. I think D5e is a better choice for the name recognition.

Traveller -- again, not familiar with the latest version, but I think of it more as an intermediate system -- works best if you are already familiar with RPGs.