Use only archival materials.
Insist on an archival hinge mat. This will include both a hinge made with archival tape from the backer to the front mat at the top, and a hinge attaching the print to the backer as well. I would steer away from foam board backing, but if the framer insists on foam board backing be sure it is archival foam board.
Choose only white mat boards.
To show you have good taste and to best present photography, mat it on a shade of white. Colored mats on photography are considered cheesy by anyone who knows what they are doing. Double overmats are okay, but not necessary.
You can be flexible with the frame.
Most photography is framed with a black or gray frame, which also goes with everything, but this is not required. You can get creative with the frame color or materials if you wish and match your décor this way rather than with the mat.
Don't use glass, use UV plexi.
This is probably the most important note: be sure to use 100% UV plexiglass, not glass. A framer may try to talk you into glass as it is usually cheaper, easier for them to get and has a higher markup. However, the best museums and galleries use 100% UV plexiglass. It protects the print from ultraviolet light and, just as importantly, it will not shatter and destroy the print if it is dropped or falls off the wall.
Carry the finished piece carefully.
A framer will take pride in telling you that once a print is framed, carry it only by the hanging wire on the back or by the sides of the frame. Never lift it by the top of the frame. This could damage the frame and/or the print.
Wisely choose the location for display.
Obviously, hang prints away from direct sun. Most people know this. What most people don't know is that to assure long life of the print, do not hang it anywhere across from a window or where it will get any light from the sky. The sky radiates UV light. If you can hang it where it will be well-lit by good track lights or other quality daylight equivalent lights, you will be able to enjoy the full range of colors and qualities in the photograph.