My beater bike is a has a basic 6 speed freewheel although I'm running a triple front chainring as well. It works fine although there are a few things to consider. The only 6 speed freewheel I've seen are 14-28 and in some rare cases you may be able to find 14-24. That's it. Thats your choices. A hub for 6 speed will also be spaced for 126mm rather than 130mm. If you have 130mm rear spacing I would recommend looking at 8 speed. They were pretty durable.
The dish on my 126mm spaced, 6 speed freewheel isn't perfect but its better than on my 130mm spaced, 9 speed road bike.
Anthony