You're going to have troubles getting 3 6970's in there I can guarantee that. I have the HAF 932 and it's a no go for sure. Probably caseless is a better idea imo.

Edit: You're going to want a case with at least 9 slots on the back panel if you do want to go with a case.

You're probably looking at something like this http://www.newegg.ca/Product/Product.aspx?Item=N82E16811119225 tower....but again it's $200 that's probably not necessary.