The general issue is making working parts you can dial in to fit and dialing in to each process. Unless you already know all the details about how to tolerance and design for a process or machine, I wouldn't expect good results. If your parts are ultra simple, sure you might get away with just having someone make a thing. If your parts really need 3d printing and utilize its design possibilities, you're probably going to need many iterations. Each material behaves differently and requires tweaking the design accordingly. No service can effectively do this for you. They can add little elements to make something printable, but they can't troubleshoot and test fit with your final assembly and application. This is why I would never outsource like this. Something like machining is different. With that you can set and test tolerances. With printing, altering the final tolerances usually involves altering the design substantially. If you dial in a FDM print first, you might get away with tweaking it for another process. If you have little to no experience printing, I would greatly limit my expectations. The delay is probably because the prints failed and they just shipped the best they had.

I didn't mention what type of printer to get. If your particular situation makes getting a printer not viable, then don't get a printer. I was just asking to see if I, or someone else, could help.