Aftermarket receivers are pretty expensive. You can pick up a new or used 10/22 for less than a stripped receiver, and you want the trigger group unless you want to buy a Volquartsen trigger group for $200. Aftermarket receivers may be steel with integral scope mounts, but again, it depends on what you want to spend. I think I'd just buy a 10/22, but in its cheapest form. If you get REALLY into it, build a second gun with all custom parts later. It'll cost even more than mod'ing up a 10/22.
Magnum Research sells high-end 10/22 clones for a good deal less than Volquartsen, and they're really nice. But if you want to fun of building the thing, you miss out on that. I think they sell just the receivers, too, but again they're more than a basic 10/22 even brand new, and they don't include a lot of parts that work fine stock, like the bolt body and the trigger group.
Generally, you'll buy a stock and barrel at the same time, since the barrel won't fit in the base-model stock. Otherwise, though, you can do one thing at a time. Like you could upgrade the trigger and leave a base-model 10/22 alone. Then you could add something like hold-open and an upgraded extractor. That would total a bit over $100, and you'd get familiar with the innards.
Then, put on a nice scope. Get that all worked out. Once you have a good trigger and a good scope, you'll be able to take advantage of a match-grade barrel.
Then you can look around for stocks and barrels (sometimes sold as combos for a price cut). There are space-gun stocks, and plain ones, walnut, laminate, thumbhole, rubberized. Depends on what you want.
If you want a target rifle up front, get the Magnum Research or Volquartsen. But if you want the fun of building it out, get a stock 10/22.
No matter what, expect to spend a little cash.
Me? I bought a Marlin 60 on sale for $120 new with a laminate stock, and I'll mount it under the scope that's now on my bone-stock recessed-synthetic 10/22. The 10/22 has aftermarket fiber sights; it will become my open sight under-the-seat rabbit/can gun. The standard carbine stock is totally wrong for a scope, even a small one mounted low, but it works fine with irons. It's also plenty accurate for iron sights, but a good scope makes you want a big fat target barrel. The Marlin comes with a heavy barrel already, though not as heavy as people put on their 10/22s.
I'm building an AR-15 with my play money, not a 10/22. About the same cash outlay, but I won't be able to afford to shoot it as much.
