I had surgery first and like the posters above, was pretty well recovered at six weeks. The radiation then undid a lot of that recovery and I became very stiff and swollen again. It has been a little over six months since I finished radiation and I still have stiffness and swelling along my scar and in my shoulder. It continues to get better with time and exercise. I know I have seen people post who had radiation prior to their neck dissection. I'm not sure what the difference would be other than slower healing. I was eating pretty well within a week or so of surgery (soft foods because I had tongue surgery, too) and would have been able to go back to work at an office job around a month out if not for radiation. Overall, the surgery and recovery were easier than I expected. I'm not sure how long your surgery will be. Mine was around 6 hours but I had a bilateral neck dissection and a partial glossectomy, so yours will probably be shorter. I went home on the third day but I still had drains in my neck. They came out on day five, I think.
I hope your surgery and recovery go smoothly.