I had both my medial and lateral menisci shaved on the same knee at the same time.
Are they reattaching yours or are they cleaning it up? If it is a clean up job its really easy recovery. Hell I walked out of the recovery room on my own, no crutches or help. I have had an ACL reconstruction though so this seemed like a breeze.
I kept it easy in the gym for about a week, and slowly started to add in BW squats and single leg movements to get ROM back as quick as possible. As I understood it, I could not damage anything else, I just had to wait for the swelling to subside to start lifting again. Hell I played full court basketball 3 weeks after surgery. This is coming from a 290 lbs thrower at the time, no skinny punk. I think I squatted 315 or so for reps not too long after this.
Its more about your healing capabilities, pain tolerance, and strength levels before surgery. The stronger you are before the faster you are going to heal. The single leg movements helped a ton for me to balance out any weakness.
I am not a doctor so do whatever your surgeon instructs you to do. In my opinion it is an easy recovery. Take it slow and make sure you have Full ROM before you push any weight. Do whatever your PT and surgeon say.