I'm looking for games like Aurora Feint (even though they're gone now), Sorcerer of Fortune, Dungeon Raid, etc. The "match three" + RPG style games I find fun because you get the RPG elements, but you can play quick games. I like Sorcerer of Fortune, but was hoping to find some others. I'd like decent graphics (Dungeon Raid, I think it's the one, has very low graphics, like 8-bit-y and you don't really have a 'character'/'avatar'). I'm also looking for different games where you have a personal character/avatar that you upgrade/customize, but that you can (preferably) see. Like, Castle Age, which I play, is nice, but I like Pocket Army where you can see your character. I'm all for free games, but they don't necessarily have to be.
How about Castlevania Puzzle: Encore of the Night. It has the leveling up and equipment and stats that you seem to be looking for. And, you can see Alucard as you are fighting. Imagine Street Puzzle Fighter with rpg elements and Castlevania characters.
PuzzleQuest 2 is still available -- not sure what happened to the first one. I would check out Legend Four. It's like Dungeon Raid but with better graphics, actual characters and story, and animated combat. It's free, but so far I haven't seen the need for IAPs.