Do you absolutely have to change the barrel or can you use the one that's already on the 10/22? Also, does any AR-15 handguard an accesories will fit on the Nordic kit?
Might be considering to buy a similar setup(and that's all your fault).
I'm assuming you don't want to replace the barrel because of cost considerations? I plan to use the factory 18" until I locate a Tactical Solutions 16" featherweight threaded barrel (and my wallet heals a bit). I suspect it's going to look a little dorky until then, but whatever - it'll still shoot.
You can save some money by buying lesser parts and then buy/sell them over time too. For example, these freefloat handguards are about $65 to get you started.

They come in 4", 7.2", and 12.5"