The borderlands games (BL2 is probably my favorite) are really cool. They're a fps with heavy rpg elements like leveling up, upgrading your weapons/abilities while blasting your way across the planet.
The Mass Effect series is also one of my favorites and the Gears of War franchise are great too. Just get the ones that are part of the main continuity. I forget which one it was, but one of their games that was lime a side story or something sucked it pretty hard.
I had a lot of fun with Destiny also (the co op stuff, I'm not into gaming for hardcore competition), and they just came out with Destiny 2.
A great, inexpensive game you can purchase in the marketplace is Shadow Complex. It's a side scroller in the spirit of Metroid and is done very, very well. I've been out of hardcore gaming for quite a while, so I'm not familiar with some of the newer titles and franchises but those few I mentioned are solid recommendations.
*Edit: The
Xbox forums are a great way to find the best games suited to your tastes. The folks are very helpful over there and you can make some friends to add to your friend's list for online gaming.