If your dr. is saying it should be done, then I wouldn't wait. The older they get the more difficult the recovery. My daughter was 5 when we did it. The recovery is about a week. The first two days there is a lot of lying around. Day 3 & 4 are a bit more painful, but then she got better everyday after that. I stocked up on movies she had never seen before. She ate a lot of applesauce, pediapops, pedia chocolate milk, oatmeal... anything mushy.
Your son's size and food pickiness shouldn't be a factor. Just keep him hydrated and make it fun with frozen yogurt and ice cream too. We have a slushy machine, so I made the ultra-fine ice and mixed it with juice. She loved it!
My husband has sleep apnea... snoring, gasping for air, etc. He should have had his tonsils out when he was young but had it done as an adult. The recovery was hideous.
The only thing I'd warn you about is when he comes out of anesthesia he'll be a little disoriented. I guess their eyes can see before their brains tell them what they are seeing and it is a little frightening. My daughter was screaming and thrashing around and calling for me. Then she'd look up and see that I was holding her and calm down for a minute or two and then start screaming again. That went on for about 20 minutes. It doesn't happen to every patient, but just be ready... it was a little frightening for me. In hindsight I would have worn comfortable pants and shoes that I could kick off quickly because I crawled into her bed with her.
Also, ask if he should have his adenoids out too. If they are going to be in there it should happen all at once. You wouldn't want to have to go back and have that done later.
Best of luck. Hang in there. It really is a very common procedure. It's not the most comfortable thing, but it's worth it.