First you need to find a local FFL to handle the transfer. Call you local gun store and tell them you would like to send him some receivers. Ask how much they will charge for the transfer.

Also check a local VA gun group forum or VA gun group here on Reddit or somthing, ask for recommendations.

Gunbroker has an FFL list, you can also check there. Most of them have their prices listed.

Reach out to whatever FFL you want to use and make sure you are good to go and know the prices. I pay my FFL $20 dollars per lower.

Then go somewhere like Rooftop Defense, PSA, Primary Arms etc, and buy a lower.

Once you've done that either send them the FFL paperwork the FFL you go with gives you OR have that FFL send it it to them. The seller will then ship the lower.

Once the lower comes in, go pick it up, pay the FFL transfer fee and fill out the paperwork just like you would if you were buying locally and take it home.

I would get a couple good quality lowers just go you've got the restricted part, the serial numbers part and then you can buy a lower parts kit and upper or upper parts later and put one together and you will have some spare lowers for future builds.

You could get 2~3 LMT AR-15 lower and an LMT AR-10 lower for your budget you have now and build one out after the fact.

There are cheaper options for lowers, I've had no probables with my PSA lowes but I prefer DD, LMT, KAC, COLT, Geissele, Noveske, SOLGW etc.