Years ago I bought a puma 92 44mag. It's not a side ejection, but I've never had any problems with it ejecting out of the top.
The H&R is the cheapest 44mag.
The Puma 92's have the good looks.
The Marlin 1894's lever look, but with a scope.
The Henry big boys are a fine lever action, and the price shows it.
The Rugers are the only option in a bolt action.
With my puma 92 I feel comfortable with shots out to 150 yards max because that's where I practice out to. At the same time, I know my shot won't be close to 100 yards so the longer practice just reinforces good shooting techniques.