I buy clays at the local gunshop. They're so cheap, it's silly. Even at the stores that traditionally have high prices, they seem to be cheap.
Unless you're shooting "hand trap" you don't really need clays as they're part of the price at Trap Clubs. 3.50 buys you a round of trap around here if you supply your own (one box of 25) ammo.
For ammo, I buy at the local clubs if I can. Watch for sales at Dicks or, if I have to (ie desperate), I'll buy at Walmart. A "value pack" is around fifteen and change for 100. Anytime I can get a case of number eight for around 40 clams, I buy.
As far as brand, I shoot anything that's cheap. Lately I've been using Estate which is kind of dirty for a gas gun but no problem at all for my old Wingmaster pump. In fact, I just got in from a round of 100 sporting clays and the gun was cleaned up in about twenty minutes. 870's rock!
The only brand that has ever given me trouble was the cheap Winchester value pack stuff. The White Box Winchester was fine but the "value pack" is not so nice.
Good luck and welcome,
Mike