Good games I can get on the app store?

I love games where you have to build your way up, purchase equipment upgrades, stuff like that. I would prefer the games to be free. Here are some examples of games I currently enjoy that fit this theme:

CSR Racing ( you have to race to get points and then spend those points on car points )
Spiderman Unlimited ( like temple run, but more recent and much better. Try to collect all the characters )
Bike Race ( I don't love it, but its simple and I play it sometimes, try to collect all the bikes. )

That kind of stuff. I use iPhone, not Android.
I am not looking for city building games such as Clash of Clans and Game of War.

Any suggestions?

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