Get the 22-250, no doubt about it.

The .17Rem is not a very commonly chambered round. I think Remington chambers the M700 in it, but I don't know if anyone else does, unless you get your chosen rifle rebarrelled. Thompson/Center probably offers a .17 Rem barrel for their Encore, or you could get a custom barrel from a place like Bullberry. Another problem with the .17 Rem is that, at least in my area, there isn't any .17 Rem ammo on the shelves of any local gun stores, and you'll probably have a hard time finding some too unless you order it online or are lucky to have a shop that stocks it.

22-250 on the other hand is a very popular cartridge (it's in the top ten best sellers in the U.S.) because it has a solid reputation for accuracy, velocity and effectiveness on varmint and predator sized game. Every manufacturer chambers almost every model rifle they sell in 22-250, and the ammo is cheap and easy to come by. I think my local Gander Mountain stocks 5 or 6 different varieties of 22-250 from the big three ammo makers, and I can pick up a box of 40 Winchester USA 45gr JHP's for $17. I don't think they stock .17Rem at all, at least I've never seen it. Also, if you plan to handload like you said before, there isn't a great selection of .172cal bullets to be had for the .17Rem, while every bullet maker makes a wide selection of bullets in .224cal, and they're cheap.

Another thing to consider when choosing between these two is performance. The .17Rem seems like a real screamer, but it's only launching a 25 grain bullet to just a bit over 4000fps. The downside is that that tiny little bullet has a very low ballistic coefficient (BC), meaning that it's going to shed velocity very fast and be very susceptable to any little bit of wind. It's also going to lose it's downrange energy as fast as it sheds velocity.

The 22-250 also isn't the most stellar performer when the winds blowing hard either, but it's quite a bit better than the .17. There are loads that are just as fast as the .17Rem's 25gr load (I've chrony'd the USA 45gr JHP's at a mean of over 4000fps), but my 250 really shines with 55gr loads which all leave the muzzle at a shade over 3700fps. It also hits a lot harder at any range and shoots just as flat, or even flatter as the range gets longer because its bullet is going to have a little higher BC. And recoil isn't really an issue since, while the 250 has relatively speaking a lot more recoil than the .17, it's still pretty negligable. Especially in a varmint weight rifle.

For more info on each of these cartridges go to the following links:

http://www.chuckhawks.com/22-250rem.htm

http://www.chuckhawks.com/17Rem.htm

Mike