You're uncomfortable with D&D... so I'll recommend relatively straightforward games that have good rules, excellent support, and are fun for me... and avoid the whole D&D paradigms of Dungeon crawls and Class-and-level play.
I would recommend any of the following:
Edge of the Empire - The Beginner's box is $30, and is a paced instruction adventure for both GM and players. Further the adventure is actually decent, and the follow-on is nicely done as well. What it is missing from the full rules is about half the combat options, and character generation. The full Core rules are due out "soon" - within the next couple months as of this writing. Note that I drafted a short article on faking Character Gen, "Faking CGen", hosted over at RPGGeek. It's Star Wars meets Firefly... smugglers and ne'er do wells in the Star Wars universe.
Mouse Guard is another excellent option. Rules light to medium-light, highly structured play, and while thick, elegant. The rules are straightforward, and the setting incredible. It helps to be familiar with the comics, but it isn't essential. While character gen is included, play it with pregens first...
Pendragon Another medium-light rules game... very thematic. This is dark ages fantasy with a realistic, Arthurian edge. If you want to check out the mechanics cheaply, Book of Knights (for 4E, not to be confused with 5th ed's Book of Knights and Ladies) is a $5 PDF, and very short form introduction to the setting. It's a fully playable rulebook, too. And, even if you later buy the 5E rules, 4E character generation is preferable to many players, as 5E has done away with the random rolls. Also note: aside from character generation, the mechanics are pretty much the same throughout the line. If you want a magic system, you'll need the 4E core rulebook, which is available in PDF (or used).
With both Edge of the Empire and with Pendragon, there is extensive setting canon - don't let that scare you. Just pick a point, and say "all bets are off once play begins"... Some of my most memorable games have been explorations of holes in Star Wars canon and breaking the Pendragon Canon. (Where were the rest of the fighters from the Death Star? Fighting my PC's and their 4 squadrons away from the Death Star while 4 squadrons of ships attacked the star! Or Preventing Arthur from doing certain damned fool things...)