I was going to post 15" rigid mountain bike but FrenchFit beat me to it. I have 3 rigid steel early 90's mountain bikes and they ride well, have quality frames and were inexpensive.

In fact one of them I bought in '91 and was the bike that got me into commuting when I pulled it down from the rafters a little over 5 years ago.

If you want a rack depending on the frame you may need to use some of the problem solvers hardware to attach it but don't let that hold you back. You could get into commuting fairly inexpensively this way and figure out how you'll like it....then eventually get something different because we all know new bikes bring great joy.