I tried to do all the side quests, contracts and hunts before finishing the game, but I got tired of running around and kept going with the main story until I finished the game and I guess I missed a lot of secondary stuff.
You can do that just fine. It's a nice story. And, if someone has the patience or really enjoys doing everything, he can do that.
I started a second playthrough trying to do everything but I got bored very fast.