There are lots of "Hybrids" that will work too. And many of them are dirt cheap. At least before you start adding parts
Here is my recent build. Drop bars with bar end shifters, but you can imagine different bars.
The basic bike was an older Jamis Coda that I picked up at a Thrift Store for $50. Double Butted Reynolds 520 steel frame. Rigid fork.
It has had quite a few updates, and has a few more updates planned. It does have rack mounts for a front rack, but they didn't match my rack

Hopefully I'll get one set up later. I haven't been very heavy yet, but so far it feels quite stable with moderate rear loads.