You could not get a better first handgun than a S&W revolver. That said, unless you get a smokin' deal on a 44 Magnum it would be less than optimal in many ways.
As a non-reloader and non-wealthy young guy, you will shoot and enjoy a 22, 38, or 357 magnum much more readily.
A 357 Magnum with a 4" to 6" bbl and adjustable sights is the most versatile handgun there is. Factory 38s are inexpensive and plentiful. Light 38 target loads are good on small game without destoying much meat and full house 357s are adequate on deer sized game. The 125 Gr 357 is a statistically proven manstopper as well.
My best advice is to put yourself in the market for a good older L-frame or N-frame 357 magnum. Finish and bbl lenght can be a matter of personal preference.