I'm going to suggest a whole other course.
Instead of buying JUST a gun look around at what competitions are being shot in the clubs in your area. Go attend a few of them to see what they are like. THis includes any handgun related local club only special events, IDPA, IPSC, USPSA, Cowboy Action and any others. Figure out which looks like it would suit you and get a gun, if you don't have what you need already, and the gear to support it and jump in. Some local club events that I have around here are a monthly speed steel match at one club and I understand that another holds hand gun Steel Silhouette matches a couple of times a year. But your area may have other options.
Putting holes in paper with any caliber, and yes this includes even a 500S&W, gets old and boring really quick. But toss in a day at the range with a bunch of like minded souls and and RO with a timer behind your head and suddenly there's a bit of adrenaline and some point to it all. And that makes shooting ANY gun, even the poor lowly .22's, more fun.
So check it out and see what's out there.
Having said all this I have read that the compromise barrel bore size of the 9/357 Convertable has led to some accuracy issues when shooting certain size bullets. So all in all if you're going to go for a single action I'd say jump right in and just get a pure .357 or go up to the .45acp/.45Colt option. At least with the .45 Convertable the bullets share a common bore requirement.
Or dive into a .44Mag Super Blackhawk. It'll pretty well make you get into reloading soon since the cost of .44Mag ammo is high. But you can easily set up a basic reloading setup for around $100. You'll easily save that much from loading .44Mag within the first 400 to 500 rounds. And after that you'll be loading for around $10 for 50 rounds. The other good news is that you get a LOT more control over your rounds this way. You can develop really accurate loads for everything from wussy "popgun" loads for recoil sensitive friends up to full power barn burning wrist wreckers and the gun won't blink an eye.
If you go for a Super Blackhawk then look at the Hunter or Bisley Hunter to keep away from that finger punishing Dragoon style trigger guard found on the basic Super Blackhawk.
