What to do!

Hi, I'm 20 years old and umemployed. I dont have a social life and the friends that I made at college we no longer keep in contact. I have a diagnoses of autism, anxiety and depression. I dont go out anywhere far and everywhere I do go is with my mum, we go to places such as shopping and restaurents. 

After finishing college in June, not having a single friend to talk to since then has been hard. I am thinking of joining a gym, to loose a little weight and to not to be so lonely. I issue is, I get so nervous when I got to speak for myself, I start to talk really fast and my anixety really shows. After knowing what to expect, I think i'd be fine. It would make it alot more comfortable for me if I had a friend to go to the gym with, but I dont think thats going to happen. Days go by and I am getting bored of just being stuck indoors doing absolute nothing. I would love to have a gym buddie to go with,  but.... thats life on the spectrum for you. 

I've tried applying for a number of retail jobs but no luck. So my question is, I am really considering joining the gym soon, but I really dont know what to expect. You know, what do I do when i first walk in? Where do i go? How am I going to control my anxiety? The thing is, with me, once I know what the expect and once I know where things are, I'm generally ok. 

Any help would be appreicaed.