I've seen the rules for beast riding in "Stay on Target" book, but I've head that the "Savage Spirits" book has some additional stuff. What stuff? Any rules on the mount itself?

It has the same list of rules from Stay on Target for training and riding mounts. It offers a few other bits for just having an animal companion (not just a mount), such as how they may be used in battle and whatnot. A list of profiles for a variety of creatures of all sizes, not just ride-able ones.