I haven't read the entire 3 pages of responses, but here's my take:
For what it's worth, if you're going to get a single shot .410, that's a great option. I have killed more rabbits, squirrels, upland game, and dove with a single shot .410 (Iver Johnson from Eric's Cylce and Gun works) than any other shotgun I own. I STILL use this shotgun.
Yes, ammo is pricey.
Yes, range and spread is limited with a .410.
Yes, 3" is WAY more effective than 2 1/2".
Yes, it is effective.
Yes, it's a heck of a lot of fun.
My personal opinion is that you will NEVER outgrow a single shot .410, a guy will always have a use for it. You will, on the other hand, outgrow a pump .410 or 20ga with a youth stock and 20-22" barrel.
If you're looking for a pump, then I'd go 20ga. Quite often, many of the .410 pumps out there are really just 20ga receivers that have been re-worked to handle .410 shells, so they're not really any smaller than the 20ga version.
Unfortunately, the youth models are just as expensive as the adult models, so by the time you buy a youth model, then eventually replace the stock and maybe the barrel, you have as much into it as you would have spent if you would have simply bought the single shot .410 and an adult 20ga, except instead of a good rabbit gun and a good upland gun, you'll have a good upland gun with a stubby stock and a short barrel in the closet.
My Iver Johnson 3" .410 is rusted to junk, has a broken hammer spur, a cracked stock, and the retainer for the forend is long lost, so it falls in half every time I break it open to reload, and it is STILL, with over a dozen other shotguns in the safe, my go-to rabbit hunting gun every time I go out with my cousins kids and my nieces/nephews.