Really it depends on your personality. You've mentioned fear a bit. But there are other things.
For example, I'm motivated by other people. That other people lift heavier makes me want to do better, that they lift lighter makes me feel good. Also, the atmosphere of the gym makes it easier to exercise. It's a bit like going to temple to pray, or the library to read. You can pray or read anywhere, but it just
feels better doing it there. For me, same with the gym. So if I had the stuff at home, I wouldn't use it much; if I have the gym membership, I'll go.
But if you're really motivated on your own, maybe you don't need that.
As to the fear, I wouldn't be afraid. If you step into the free weights area at all to do more than little pink dumbells, you'll be one of the stronger women there. You're not going to stand out as
weak, you're going to stand out as a
woman.
Anyway, as BoyFromAus says, most people mind their own business. They also tend to ignore new people, since most people don't stay more than a few weeks. By the time you've been there a couple of months and are recognised as a regular, you'll be stronger. Plus, everyone except 17-21 year old males understand that it doesn't matter where you are, it matters where you've come from. That is, there's a difference between doing 10 pushups when you used to do 2, and doing 10 pushups when you used to do 50. People are impressed by improvements.
Also, $17pw for a gym is not a really good offer. I pay $54 a month at Clayton, and used to pay $42 a month at Oakleigh. Weren't you in Narre Warren?
This joint will probably be cheaper.