The combination should work fine together and meet most of your need.
The Badger 200G is one of the few single action, internal mix, gravity feed airbrush. I have not used one, but it should need less air than most other siphon feed beginner AB. And I expect you would get a quality AB from Badger for your money.
The Testors Mini Blue is on the lowest end of low end compressors. It provides 0.18 CFM of air. It should be fine for the 200G using thinned out paints. However, for the same price (~US$70), There are better choices. If you have not open the Testors compressor, it pays to spend a little more on a compressor that can pump 0.5 CFM up to 35 psi.
I love the 200G. Very satisfying a/b to use. Cleans easily, works well. Properly thinned paint at lower psi will spray some really nice tight lines.
I bought a compressor from Harbor Tools with a 3 gallon tank for $69. Pretty darn loud, but I can paint most of a 1/48 scale aircraft on a tank of air. Delivers enough psi I can use it to inflate the car tires too. Quite handy.