If you are going to hunt deer with the 44 and the shots will be up close and personal, I'd choose the 1.25-4x. If the shots you are going to take are quick ones and may be free-hand, I'd choose the 1.25-4x. If you will be shooting from a rest most of the time and your shots will be at greater distances, I'd choose the 2.5-7x. Here in PA, whitetail hunting is often done in the thick brush, shots at far less than 100 yards. I use a .375 Win and a straight 2x bushnell scope and it does a fine job. Target acquisition is never a problem. A 1.25-4x would be a great choice, in my opinion. For groundhogs, the .222 and a 3-12x Burris get the job done, but almost all shots are done off of a rest/bipod. It's just too hard to get a deer on the move into the score at the higher magnifications (unless rested and very stable). The option of a 7x would be expecially nice when used for sighting in at 100 yards, though...
As far as mounts go, I love the Leupold and Burris dual dovetails. Rings are Leupold. I do not use a hammer extender and it works just fine with the medium height rings (I have a small thumb anyway!)