My Son, my Daughter and my Wife each took their first WT Deer with a Marlin .357. It's a great gun under 100 yards. Having said this, if I were buying a rifle for deer hunting I'd get a .30-30. This will extend the range by at least another 50 yards and is capable, with a 170 gr bullet, of taking anything up to the size of a Black Bear. I know several Left Handed Cowboy Shooters who use lever actions without any kind of problem.
If you do get a lever action try a Buck Horn Rear Sight. They are great hunting sights, very quick to pick up your target.