Playing is free and you can really enjoy the game that way if there are any financial concerns. Or, like me, you will want to spend a bit to help hurry along your advancement.
I think it is an absolute must to buy into the Premium Account as it gets you 50% more experience and credits per battle. Runs about $9/mo or so. Then, you will probably want a little gold and that costs as little as $9/bunch as well. The "Store" will show you all the options.
Anything you buy extra only allows you options for purchasing and equiping vehicles. It makes no changes to the battlefield, other than good tanks usually beat poor tanks of the same tier. Buying stuff allows you to get "gooder" tanks sooner, that's all.