Hi, Tina
I wrote a bit about what I've found to work in another thread, but since we're not allowed to include links until we have one hundred posts and I don't want to clutter the board with repeated content, please search for the subject "Re: I don't know how to properly paint my nails" if you're interested. My reply is No.8.
Yes—cheap polishes are, well, cheap. While better products cost more they are better formulated—and as others have posted they also have higher quality brushes. A good brush makes it much easier to get smooth and even coverage.
Robin, if you want to be a bit inconspicuous you could using just a clear polish followed by a matte top coat. They are sometimes hard to find, but I believe e.g. O.P.I. offers one. (Dollar stores do too, sometimes, at least where I live, but if you go that route I'd suggest at least transferring the content to another bottle with a better brush.)