Welcome to CF! We are glad that you've joined us!
I've visited a new church for the first time, often alone, literally hundreds of times.
Of course I had the background of having been in a worship service before, even if it was a bit different.
For a non-denominational church (there are different kinds) they will fall within a certain range. If you can, you might like to find out how you are expected to dress at the particular one, so you aren't uncomfortable if you guess that part wrong. If you can't find out in advance, business casual is usual middle-of-the-road enough to fit in most places (as long as they are at neither extreme of casual or formal).
Beyond that the level of attention you will get depends partly on how large the congregation is. The smaller the congregation, the more notice you will get. In a medium sized congregation (at least several hundred) you can begin to go more unnoticed if you want.
As stated, the easiest thing to do is whatever everyone else does.
The greatest majority of services will have a session of music followed by the teaching/preaching.
What kind of music will vary. The older hymns that people stand or sit in place and sing are becoming rarer. More common are the "contemporary praise and worship" where some stay in their place (usually standing), some may gather at the front. People may or may not raise their hands or dance. I have seen a smaller percentage of others though that had performance dancers, or hard rock bands, or laser light shows, or a full performing orchestra. It varies a LOT. People may follow a prescribed stand-sit-sing-silent or may move all over the sanctuary and dance. But most often I have seen where people are free to remain in place and a few come up, and you can sing or not. It's usually easy to do whatever you're comfortable with and still fit in.
And the teaching/preaching part is easy from the congregant's part.
There are often invitations, prayers, times of praying for people, etc. Again you can usually do whatever makes you comfortable.
Sorry ... I've been to SO many churches, and so many of different kinds, but probably about a hundred non-denoms included. For the most part, they likely won't do anything that will shock you (though realize that if anything DOES bother you, it almost certainly doesn't represent every church out there) ... and it's unlikely that you would unwittingly offend them or stand out in any bad way.
You'll probably find afterward that any general anxiety was nothing to be concerned with, and if anything particular should bother you, it is often unique to that particular fellowship.
I can understand it's worrisome, but you'll probably find it much easier than you might be fearing.
God be with you!
