Try to find a knife that is roughly the same weight as your tomahawk. Having it the same length is also a great help, in that they will both throw about the same, if they are physically similar. Release the "hawk" naturally - don't stop you swing, or try to introduce spin...it'll spin about it's centre of gravity naturally. I like a handle that is roughly the same length as my forearm. If it's too long, it takes longer to revolve, forcing you to stand further from the target. Make your throw deliberate...don't be tentative or afraid of hurting something. At the same time, you don't have to throw it hard...it has lots of mass and will stick deeply into the end grain of a log target with a moderate throw.
Our tomahawk course has mostly one turn targets, but there are targets that require a turn and a half, and two turns as well. We throw the knife at the same time, and you are not allowed to remove one before throwing the other, so accuracy is important so as not to cut off your own handle. For that reason, I always throw my knife first. I am less likely to damage my knife, and put myself out of the competition, than if I throw my tomahawk, split or otherwise damage my own handle and make further throwing next to impossible.
For the time being, just throw one or the other. Good luck and have fun.