What Period do you want to do? If someone wants to do Americans, you can do Mid-War or Late-War. If you are planning on playing with local group already playing
FoW, I would suggest you look into what they mainly play (
LW is the most common, but it is sometimes
MW).
I can't really give you much advice without knowing the period, but $60-75 will not get you much for a Soviet infantry based army because, as you said, they work with weight of numbers. Because of this, you will start with less points-wise than your friends for your money. I would suggest the Plastic Soldier Company for the majority of your needs, (best store for them in the US:
http://www.thewarstore.com/theplasticsoldiercompany15mmscale.html ) as they have very cheap and good plastic tanks, and they also have cheap Soviet infantry ($25.99 for 130 figures).
As to balance, all armies (in the same period, of course) are pretty well balanced against each other. With the amount of tanks you are playing against, though, you will likely have some difficulty. To counteract this, you should have a good amount of anti-tank guns and maybe some tank destroyers (like SU-100s).
I don't know if you will be able to start with all that much for $60-75 each. For starting, you can get the $60 rulebook bundle, which comes with basic lists for America, Germany, Britain, and the Soviet Union. This site:
http://easyarmy.com/ will allow you to play around with making lists using the forces book that comes with the rulebook for free, all you have to do is sign up.