Free apps often use advertising services or other constantly-running services to make money. I've found that sticking to open source free apps or buying an app usually makes me happier in the long run than trying to deal with free apps.
One good source of apps is bundles. There's many places you can get apps bundled into a single Pay What You Want price. For example, in the latest Humble Bundle I paid $10 and got 8 games, some of them very highly rated. I can install them on my PC and my Android tablet. Here's a wikipedia link:
https://en.wikipedia.org/wiki/Humble_Indie_Bundle