I like the set-up where I work, the American Psychological Association in Washington, DC. We have a copy center/print shop and mailroom in-house, and both can help with printing and distributing projects, and can also work with vendors outside of APA when additional support is needed. This gives us great flexibility and options. If it can't be handled in-house, it can be sent out, and estimates can be requested from a number of vendors.
I'm including our in-house form below as some of the things mentioned may be helpful to think about. It doesn't cover everything but is a good start. With staff in the building, it's also easy to communicate face to face and by email.
I find that communication is key. It's important to maintain a good, friendly, professional working relationship. Ask questions and communicate about what you want. Allow an extra day or two or more if possible since no one likes to be rushed and equipment can be busy or down. Make sure your project is as ready or final as possible or changes will cost you. If you are good to them, they are likely to go above and beyond for you.
Vendors that we've worked with and had good experiences with are Doyle Printing in Hyattsville, Alpha Graphics at Tysons/Falls Church, and Accurate Printing in Woodbridge, VA.