The 5770 is NOT a long card, ant that is a mid tower case. You will have no issues.
For $200 you can also get a 4890 or an OCed GTX260, both outperform the 5770 if you don't mind a DX10 card. I believe the 5830 comes out on the 25th which is only a few days. It might be worth waiting as I think it should fill in the gap between the 5770 and 5850. should be priced around $200 or slightly over, but would potentially be your best buy.
PS, the 4870 is overpriced almost everywhere I look. I wouldn't buy it for anything over $140.