If you must have a revolver and you may only get one, then the clear choice is a Smith and Wesson 686 or 686 plus.
If you have a less constrained budget, then get one of the eight round 357 magnums.
357 is a deadly round but still manageable, and you always have the choice of loading 38 special or 38 +P. You can also use 38 for target practice and 357 for self defense.
Barrel length depends a lot on what you plan to use it for. A snub nose is concealable but the flash and report will be awful. A 4 inch barrel is ideal.
44 magnums are fun, but not practical unless you are in places with bears or moose. And even in those cases a handgun is grossly under powered. It's just better than nothing at all.
J frame revolvers are a fistful of dynamite, especially with 357 magnum rounds. They hurt like hell for any period of prolonged shooting. For a pocket pistol you're better off with a small 9mm or 40.