mojoe: yup, gotta agree with PartsMan, .357 Handis are neat and fun to shoot. Do you handload? If you do, you'll enjoy the cartridge even more. Several members here, myself included, report their .357s have very long chamber throats. Most of us have found that we can chamber .357 Dan Wesson cases in the factory chamber, and many of us have lengthened the chamber to .357 Maximum. I'm still wringing mine out, trying different bullets and loads. The ability to tailor your ammunition to the chamber is a big help in achieving accuracy.
As far as power goes. the standard .357 round is adequate for whitetails at shorter distances, 50-75 yards. Use a good bullet -- Winchester makes a round for handgun hunting that should do the trick. But if you handload, your .357 Handi can utilize bullets that are not available in factory ammunition. If you aren't handloading now but are interested in getting started, plenty of members here will give you good advice. First step is to get a good, recent bullet manufacturer's reference book. Hornady's, Speer's, or Sierra's are all good. Read the introductory chapters carefully before buying anything else, and start slow.
I find that handloading is almost as much fun as shooting!