I want to go to the gym but suffer with bad anxiety, please give me some advise?

Go there are start on the treadmill or a bike. That way you have lots of time to look around and see how other people are using the machines. Then when you use them you know how they work. Start with light weights and do three sets of 8 to ten, very light. You can always increase as you go, but do not overdo the first time.
For legs and bum the stair climber and eliptical are good. You should do upper body too on the weight machines.

As for looking at you, in my experience nobody cares and nobody is looking. The big muscular people are looking at themselves only in the mirror and the rest are sitting on machines playing with their phones. So get in there and get fit.

If anyone is judging you, you know for sure they are insecure about themselves and taking it out on you. Case in point, this chubby guy benching a full wagon wheel, probably for the second time in his life. I could tell he just barely crested a threshold of "in shape" after being a big fatso for a long time. A current fat guy newb is arm raising 3lb plates to keep his muscle warmed up during a rest, which is valid. The less-new newb says "you need a spot?" Making fun of the new newb for the 3lb plates not being heavy. From the outside, you can see who the jackass in this situation is.

The other day I saw a few friends being a little goofy and breaking alot of etiquette rules. This woman who I thought to myself in passing "now there's a bad bi*ch" knows as well as I, they just have to learn for themselves. She tries to subtly hinder their lingering by asking "how many sets you got left?" And it worked.

Like kid playground bullies, they exist and even bashing their heads in doesn't stop them, it just puts you in jail, leaving them with nobody strong enough to stop them. Adult playground (gym) bullies exist too and for the same reasons. Nazi's, sexists, and liberals, all think you shouldn't exist for the way you fundamentally are. Are you going to hide away in the house forever because of the fact they exist? If so, they have power over you and that tension will come out in another way that makes you a dick. And the cycle continues.

My advice is to hire a trainer. Your trainer will teach you the equipment and start you on a program. Your gym might provide a free orientation with a trainer. Otherwise, don't join. Walk around your block and lift weights at home. You won't feel comfortable at a gym if you aren't used to interactng with people at close quarters. When you get a whiff of those keto weight trainers, you'll flee immediately. Best to join planet fitness.