What are good places to make boards. I'd like to send gerber files and get a populated board. Do I have a choice of sending parts or having them purchase parts?
Where on this big planet are you? This does make a difference.
What kind of quantities?
Bare PCB fabrication and assembly are usually done by different companies although there are "turnkey" manufacturer's who will contract-out the fabrication and purchase the components.
Turnkey manufacturers can also test the board but you have to work with them to create a test procedure, specs, and any specialized test fixtures/equipment.
In addition to the Gerbers, you'd have to supply a bill of materials and probably an assembly drawing. If they are buying the components you'll have to supply a list of approved manufacturer's part numbers.
If you supply the parts and they do the assembly/soldering it's called "consignment".
Small batch assembly is expensive the set-up costs might be more than $1000.
I use JLPCB at jlpcb.com for my boards and they have asked about assembly, I never had my boards assembled outside of my lab.
Try Screaming Circuits in MN. You can send parts, or they can purchase to a Digikey parts list, with other components as needed.
They get boards from a US supplier in AZ I think, or maybe OR.
I am also used jlcpcb for my board. It is fast and reliable.