Honestly, Central America is the best country for America:Homefront not only does it use the axis doctrine but the only other player nation next to you is South Mexico and the border that you share is only 3 provinces meaning that you can build fortifications without crippling your economy first day. Panama should be a day 1 objective so that any country in South America cant attack you early game without a costly naval invasion which will almost 100% fail for them, you don't have to take the whole country but at least get Penonome. The economy is very good and the only economic issue you will face late game is manpower which everyone else also faces. On top of that you have 2 close Ai nations that you can quickly take to boost your military power (I don't recommend you go for both day 1). Think of something like Missouri which has 7 nations that border it, you're dead meat if even 1 attacks you since players like to go for easy targets in the early game meaning that if 1 attacks, then the rest will most likely attack as well. The only major downside to going for Central America if that Mexico is full of mountain terrain meaning that expansion will be significantly slowed. Another one is that invading South America will just as hard for you as it is for the enemy meaning that if you do attack South America, expect a war of attrition (unless you use your navy to wipe out their fortifications and units on the shoreline which can easily give you an opportunity for a naval invasion, the same thing can happen to you as well though so be sure to have naval bombers and Interceptors close by just in case.

I mainly use artillery, infantry, medium tanks, and armored cars and my main land units (Since I unlocked all the blueprints for them.
I use every unit in the aircraft tech tree
I sometimes use rockets when I don't want to risk losing strategic bombers