I'd like to chime in with the opposite viewpoint (not to say there's anything wrong with this idea). I don't find shooting .44 Magnums fun. I still have a scar on my knuckle from an old Blackhawk with a square trigger guard so maybe I'm traumatized, but I find .44s tend to get shot a little bit, admired somewhat, and generally be a big heavy novelty that shoots loonies. Even if you reload, the cost is significantly higher than .357 or .38, and I wouldn't be inclined to shoot it a lot. I'm not saying "stay away from big revolvers" but rather just to understand what you're getting into with them.
When you're getting a revolver, especially your first one, consider what you plan to use it for. I know we're limited to punching holes in paper short of ATC but there's a LOT of ways to punch holes in paper. Do you plan to have a recreational plinker, or do you ever plan to get engaged in organized shooting like PPC, Bullseye, IPSC, or IDPA? I know a friend who got into Cowboy Action shooting just because he loved his Ruger Blackhawk so much. If you think you might want to consider that someday, make sure you're buying a revolver that could be used in the games you want to play. It's not necessarily the first thing to think about when you're looking for a first revolver, but it can save you some money down the road. If you want to shoot competition, beware the cylinders with more than six shots--a lot of revolver division rules in gun games make them a liability.
Personally, I think the K-frame .38 revolvers are a great introduction to wheelguns for people looking for their first one and they can regularly be found at good prices. If you can find a .357 you like, they're awesome and fun but most people shoot more .38 than .357 anyway. A Smith and Wesson Model 10 or 14/15 will serve as a great gun you'd be proud to pass down to your kids and they can be found for under $500. They're also great for most gun games, since they were the basis of a lot of revolver divisions in competition like IDPA. Older M10/14/15s also tend to have super-sweet triggers, and with .38 loads they're guns anybody can pick up, shoot and enjoy.
Also, don't discount the Single Action revolvers. As Jimmie said, a lot of people end up shooting DA revolvers SA anyway, so you can always just cut to the chase with an extremely cool gun like a Blackhawk or Vaquero.
Regardless of what you get you're sure to be pleased. Wheel guns are the real guns.