For a small order, I'd suggest working with a company that does both board fabrication and assembly(sourcing also included).
There are lots of companies who offer that kind of service. Personally, I get boards from PCBNPI (Fast Turnkey PCB prototype & PCB assembly service) and they do have an assembly service. Their service and quality are very good,while price is OK. Saves my time and money. I highly recommend.
Fair warning: hardware has a significant startup cost. In most cases, having ten boards made will cost about as much as having a hundred made. In both cases the bulk of the price is due to setting things up, you're just distributing that cost across different numbers of boards.
Jack
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