The DOA4 is fine. It just isn't good if you want to really get serious or your character requires a lot of precision or fast stick movement.
Don't get this, get the DOA4 (probably off eBay) and you'll save a lot of money (since they're the same afaik)
And yes, all xbox 360 controllers are compatible with PC, even wireless (that is, if you have the wireless receiver for the computer lol)