I began my bike commuting with single-strap backpack (like this: One Strap Backpack) When I kept it decently tight, it didn't slide around, or make me feel unbalanced...but I usually only had clothes in it, nothing too heavy. So the balance thing didn't ever bother me...I felt in control.

But I did sweat, and ended up with a wet spot on my back...(I even get that when walking with a backpack)...so once I got a rear rack I strapped the backpack to it with bungee cords and have never gone back. Way better, less sweat. It's definitely the way to go.