Google Play says in their developer agreement that they don't allow third-party app stores:
You may not use Google Play to distribute or make available any Product that has a purpose that facilitates the distribution of software applications and games for use on Android devices outside of Google Play.
As for installing third-party APKs, that's pretty easy to skip, and I could provide an explanation inside the app itself.
When it comes to the actual games, if you look at the top rated Android games today, not a single one of them is filled with ads. I've been using an early version of my app for a while now, and the stuff that's available here is pretty fun, even if there isn't much of it.