I would agree with starting with a 22LR, either a single or a double action. A Ruger Single Six, either new or used, is pretty hard to beat for the best gun for the money. In double action you are looking at pretty decent dollars for a real good one. Any of the K frame Smiths, or an old Colt Officer's Model are going to set you back a bit, but they are great guns. As far as current new less expensive models, I think the Taurus model 94 is about the best bet, but if you plan to shoot it double action you had better get a Wolff spring kit.
Once you are ready to move up, I don't see a problem going to the 44 Magnum, but you would probably be well served to start out shooting 44 Specials. A 44 Special doesn't kick any more than a 38 Special in a smaller gun.
I would go on Guns - Online Gun Auction - Guns at GunBroker.com
and look at all there is, and pricing
, and then try to get to some shows and dealers and handle a few.
A lot of people will tell you they have an Acme special or whatever, and it is cheap and fantastic, but try convincing someone else of that when you want to sell it. If you get a good name brand gun, especially a used one in good shape, if you take decent care of it you shouldn't lose a dime when you go to sell it. Something to keep in mind if you are not sure what you want to commit to forever.
Good luck and good shooting.