The Rossi stock leaves a lot to be desired. The only caution that I would mention is that it takes a little work to get the .243 Handi to shoot the way it should.
I know you asked about a .243Win., but IMHO, if you want a great accurate Handi for deer hunting right out of the box, get the 30-30. I don't know why, but they are super accurate, I have two, both assembled from barrels I purchased from members here. They shoot 1" groups at 100 yards with 150 grain Winchester Silver Tips.