I tried a number of simple mobile rogue-likes and dungeon-crawlers last night and got a feel for what I'd like to try. I will make it turn-based so I won't need to worry about event timing so much. There will be a grid for each screen so the camera doesn't need to scroll.
I remember when I started learning Libgdx, I read the code for Cuboc and it used a bitmap file as the level editor. I'm going to try doing that for this game. If each screen is a grid, I can mix and match left, middle, and right pieces to create random stages while easily ensuring there is always a fair solution. And if I use Gimp as my level editor, I can turn layers on and off to make sure all my combinations work reasonably well together before having to play test them.