If you don't already have a lower, expect to overpay for one. For a .22LR upper, all you really need is a poly lower. If you can find one already built for under $200, don't hesitate to buy it.
I always send these links out as guides, but they'll also tell/show you everything you'll need to put one together.
Assemble your own LOWER, UPPER, FREE FLOAT, TRIGGER, GAS BLOCK - Step by step instructions! - AR15.COM
:: Guides
Yes the poly lowers are rated, per the manufacturer, to handle any upper that can be put on an aluminum lower. As far as 7.62, are you talking 7.62x39 or 7.62x51? 39 yes, 51 no.
I always send these links out as guides, but they'll also tell/show you everything you'll need to put one together.
Assemble your own LOWER, UPPER, FREE FLOAT, TRIGGER, GAS BLOCK - Step by step instructions! - AR15.COM
:: Guides
There is also a good set of instructional videos at brownells.com. They have individual 1-2 minute videos for each part of the assembly process. I found them quite handy when I built mine!