How to minimize risk of software copyright infringement claims

I had a software developer create a software program, which I copyrighted and then assigned to a software company (and LLC) that I co-founded. I plan to sell the program to the general public.

Then I discovered that there's a competitor that has a program with a similar idea, although the functionality, look and feel, etc. of our programs are certainly different. The other program is copyrighted, I think, but doesn't seem to be patented.

I'm concerned that the competitor would try to drive me out of the market by threatening a lawsuit for copyright infringement (or suing and running up legal bills), even though my lawyer said that there should be no basis for that.

Any tips on how to avoid claims of software copyright infringement, or any other problems that could arise from this scenario? Thank you.

You have a little misunderstanding. In very overall, hand-waving terms, copyright kind of corresponds to owning a piece of land. You get copyright on a book, a piece of software, music lyrics, etc. You obtain copyright automatically when you create the work. You should further mark the work as copyrighted, and have an appropriate license for its use in place.

If you created software X and another company created software Y, and you didn't use the same contractor / didn't spy on each other / didn't use any shared resources during development, then there can be no copyright problem per se. You have the copyright to X and they have the copyright to Y.

Any tips on how to avoid claims of software copyright infringement, or any other problems that could arise from this scenario?

As noted above, you're probably not looking at a copyright infringement situation, you're more looking at issues arising from unclear or non-existing paper trail, or maybe at the extreme from a patent lawsuit (but don't worry too much about that, patent cases amongst 2 small startups are extremely rare). Dana H. Shultz has a good post about "Top Ten Intellectual Property Mistakes of Startup Entrepreneurs " which you might benefit from.