There are a number of funny stages you hit during this process. One is where you have SMDs that you're just trying to learn how to use, you're not sure exactly how they fit into your circuit, and you're not ready to mount them on a prototype PCB even in a run as small as 10.
Your savior here is www.proto-advantage.com. They will sell you a breakout board. They will also purchase your part from digikey, and mount it on the breakout board. They do this at a reasonable price, with fairly low delivery times.
It's the next step that's a bit harder -- having a prototype PCB that you need populated. Big assembly houses will often do this, in my experience, when they think it will lead to a real job, but you pay fairly dearly for this. It also slows things down to a crawl. It can take a house like that a week just to generate a quote for this type of job. If it's complicated or fine-pitch, they will want to cut a stencil, and they will use their own mechanism to generate a stainless steel stencil to their in-house spec, which will really add to big NRE on a small job. There will be discussions on whether your boards will be kitted, or full turnkey (that is, who's supplying the parts on the BOM).
There are smaller shops that you might be able to find that provide these kinds of services fairly routinely, but again, you'll often find the quote process can be a bit slower than somebody in a prototype frenzy wants to accommodate.
Frankly, this sort of stuff was going on around here often enough, adding a few weeks and a few thousand dollars here and there, that I tooled up with a jury-rigged reflow station -- a toaster oven refit with a Global ramp-soak controller, beefed up with some extra insulation to get some more oomph out of the heating elements, and a 10x-200x usb microscope to help deal with small parts. Hard to say if this is right for your situation, but I'm very happy that it got done. Took about three weeks of dorking around, putting in the temp controller (which many would call optional!) working out a good ramp-soak profile, learning how best to deal w/ the solder paste, ...
Total cost in parts, ~$250-$300, about $120 for the temp controller, about $20 for thermocouples (which I sort of spring-load near the biggest components on the boards), about $50 for a convection toaster oven, and about $100 for the microscope. Instructions literally all over the web.
It makes the system of using the proto-advantage boards pretty fast.
Some PCB houses even supply a free stencil along with a board. Depending on size, the types of boards I deal with usually run about $120-$150 shipped in quants of about 10, two sided, masked, with a one side silkscreen and a really nice surface finish, free stencil, with an 8-10 day turnaround.
You'll want to build a small jig to help you deal with stabilizing a stencil, if you go this route.
For maximum efficacy, a hot-air rework station would be a valuable tool. I fake that right now with a butane iron with a blower head for the two or three times I needed it, but I'll buy a cheap rework station soon.
Works great, really speeds up prototyping, and I've had no problems with components down to 0603 (and I don't have a young man's eyes!)
A problem you'll encounter if you go out-of-house is that the places that deal with assembling PCBs want nothing to do with boxing them in a case-- at least in my experience. To get this done, now you're talking about harness makers and contract assemblers. It's great to think of this stuff at the stage when you're designing your board-- it will make your Design for Manufacturability pass go much smoother. Many connector issues these days are handled right at the circuit board. I've always done this sort of prototype assembly in house. Take a look, though, at frontpanelexpress.com, particularly their enclosure service. This will be expensive (at least from my angle, maybe its a service very much worth it to you).