Great thread so far. These are good observations I'd like to build on.
I work out in a pretty average commercial gym that has a wide spectrum of customers. Newcomers like you come and go all of the time. ALL THE TIME.
Don't try to impress anyone. Do good work with your time at the gym. Don't worry about your poundages or how you stack up to anyone else in the gym. I recall one fellow who was around for maybe two months. He did a lot of stupid stuff. At the time I was squatting 3/week, so I'd start every workout by working up to at least 405x3. I don't find that particularly special, it was just the weight I was working with at the time, but it was probably the biggest lift done at that gym most of those days.
What does this fellow do? He loads the bar up to 365. On the Smith Machine. With no warmup. Then he puts his feet way out in front and bends his knees a little bit, moving the bar about four inches before somehow moving it back up to where it started. I was watching him do this and he looked at me and nodded, as if to say "yeah bro, I squat". One rep and that was it.
Perhaps that was a deliberate and controlled movement with a specific goal in mind, but it sure looked like he was just trying to show how strong he was. Except he didn't really demonstrate any great strength. He just demonstrated his questionable judgement and a fragile ego.
A few weeks ago a very skinny teenager watched me do a set of deadlifts. I got 475x8. My partner got 475x11. He asked me to leave 135 on the bar and he did his deads right afterwards. He worked up to a very nice looking set of 225x5 with good form but I could still tell it was a challenging weight.
He got a high five and I complimented him on a very nice set of deadlifts. I like to see someone doing it right and it clearly didn't bother him that two big guys had just moved a lot more weight than he did. That gets my respect.
Like everyone else is saying, just show up, do good work and be respectful. Once the regulars see that you aren't just another chump they will warm up to you a bit. Or just keep your head down and do your work if you don't want to socialize. There's nothing wrong with that, but I like to get to know the guys I spend so much time around. Lots of good times and laughs to be had while still getting good work done.
Good luck! This shit ain't rocket science.