Beginner weightlifting

A little bit of insight, I was a bodybuilder before turning to triathlon and yes I was the typical skimpy dressed bodybuilder girl hanging around the alpha males. You shouldn't get nervous around people in the gym because well, nobody really cares about you because people are usually too busy being concerned about themselves, much like you.
The big guys in the weights room will barely look at you, as you say you're not a competitor, they won't bother and most of the time they are too concerned about their own performance to pay attention to you. As intimidating as they may look, they are no danger.
I think the best is if you join a gym and have them prepare (and explain!) a program for you. And always, always, always feel free to ask help. Remember a smile and a please/thank you go a long way, everywhere.
I know at the start you'll enter the gym like holding your hands on your eyes and praying they aren't all staring at you but well, truth is they aren't. Unless you're wearing a chicken costume, in which case I recommend you don't.
As an alternative, which is really popular these days, you could join one of those circuit training classes. You get to learn to lift, workout in a similarly skilled group, get to know people...and when you feel like you can just move out and start lifting by yourself.
Just never never never be afraid of doing things wrong and be ready to laugh them off. We all do things wrong, we learn, we laugh at them and we do them better. It's what we are all here for after all, to learn and better ourselves.

If you go to the Gaining Weight sub forums, there's a post that @psuLemon wrote about lifting programs. It's a few pages back.

Have a look through the beginner programs. StrongLifts 5x5 is what I started with and it really helped me get a handle on the basics and helped me gain a lot of strength.

If you can't bench the bar, does your gym have those fixed weight barbells? You can use that and work your way up to the bar.

Do your research and watch some videos on how to do the lifts and maybe get someone knowledgeable to check your form. Form is very important. You don't want to get injured.

As for the intimidation factor, it happens but it goes away once you're comfortable and have a routine.

Good luck and have fun!

ETA: The link http://community.myfitnesspal.com/en/discussion/10332083/which-lifting-program-is-the-best-for-you/p1

I work with 2 personal trainers. With one trainer I do flexibility and movement exercises to help me with (dry land) swimming and golf (to some extent). I see the first trainer (female) for 30 minutes once per week. With the other trainer (male), I lift heavy weights once every other week. I have been doing this routine since last August 2016.

I like working with a personal trainer. I don't have to think about what exercises to do for my workout. I can leave that to the PT. He or she can judge my level, and adjust my workout to whatever training level I am at, or particular needs or things I want to work on. This is the first time I have gotten serious about strength training. I know next to nothing about how to design and execute a strength training program.

I used to think that personal trainers were too expensive. Now that I work with them, I really appreciate the benefits. I would never go back to trying to train myself, at least for strength training. Maybe I will learn enough about strength training after a couple of years to train on my own. But for now, I really appreciate my two trainers.