Hi Steph! Welcome--I think you will love this board! I also have twin boys and one of mine has an autism dx. as well. Like your son he has struggled with some digestive things (reflux, gagging, vomitting all very familiar here). My son is also a contact craver--I love his hugs--I think I've had about 30 today already. That is likely a sensory clue as well as a wonderful trait!
First, give yourself some time to sink into the diagnosis. Even if you saw it coming it is still an adjustment. It is also hard for some (was for me). How are you doing?
Take a breath. You don't have to do anything right now.
When you are ready, I'd focus on what you want to do to address the autism if you plan to use any autism related therapy. There are parents using almost every therapy (as well as those who aren't pro-therapy) on this board so lots of resources and opinions. http://www.autismweb.com/education.htm
This site has a great over-view of each of the major autism specific treatments. Floor time and RDI are done by parents. I'm not familiar with the others enough though I know some are typically done by people outside the family. Also, I would pick a few things to help with his gut/tummy issues and digestion--whatever is manageable for you both emotionally and financially. You can decide more later.
I'll tell you what I am doing realizing that every kiddo and family situation is different.
First, I am addressing the weak areas related to autism with a parent based therapy called Relationship Development Intervention or RDI. It is listed in that site above with the other therapies and I think it gives this link but http://www.rdiconnect.com/
I like it and it has already helped my son. Prior to this I did floor time (though self taught with books and such) and found it beneficial too.
Then I do some biomedical things to help him be healthy and feel better. My world in this area has been complicated. If I could rewind to your place I would start more simply. I would think about addressing some of his digestive issues with a good probiotic and digestive enzymes if he can tolerate them (Houston's Brand is great and the owner will talk with you directly at no cost and even send free samples to try). Start the enzymes very slowly. These are easy things to start. Later if you are up for it you might try to cut out all dairy and all gluten and see if there is improvement. There are lots of diets out there..I've tried most of them.
As far as supplements, I give my sons carlson's cod liver oil--good for both boys and you too actually! I do particular vitamins and some other things with my sons too (both actually--I do almost everything that I do with Andrew with Caleb as well) but I don't want to overwhelm you with information. Optizinc cut down for his dosage level is a well absorbed zinc and zinc can be healing to the digestive and immune system.
I found a good occupational therapist who specializes in sensory issues. That has been good and helpful. Our early intervention therapies...well, they haven't been helpful in terms of the autism itself or minimally so. We're done in two weeks and I'm glad. It was helpful, though, when he was young and my son is verbal and I think our therapists are weak so your experience may be different.
On the sleep. I do use melatonin with my son but I use very low dose and I do not use it every night. Kids can build up a tolerance so you might take a break and then go back, using the smallest effective dose (my understanding is that small doses are less likely to build tolerance and also less likely to cause waking as it wears off) and taking breaks periodically. I know melatonin doesn't work for everyone but since it did with him originally I hope it will again. We have sleep issues here too and I really haven't found the answer. Naps are particularly a problem here though it is less so than it was at your son's age (just because as he gets older going without a nap doesn't mess up his night sleep as much as it did when he was young). I'm experimenting with some sleep stuff now. I'll let this board know if I find anything really useful.
Again, take time to just be. You don't have to make a ton of decisions now.