Would running a band saw or cnc machine in my basement be safe?
My grandfather was a carpenter and when he retired he moved most of his tools into his basement. This included a drill press, bandsaw, and a very heavy full size table saw. It is definitely doable.

Drill presses and bandsaws don't generally create as much dust as sanders and routers. You can probably remove most of the dust they'd create with a well placed shop-vac. The bandsaw should have a dust collection outlet that you can hook the shop-vac up to. The drill press probably doesn't. You can also invest in a dust collection system to collect the dust and clean the air in the basement.

Depending on your particular basement, there are other things to watch out for.

Make sure you have a sufficient electric supply. You don't want to overload a circuit that was originally meant to power only a few light bulbs.

Make sure that you have room to move around tools, and to get out of the way if something goes wrong. Make sure there's room for your work too - raw materials and finished pieces. think about your ceiling height too, and imagine carrying and positioning an eight foot or longer board. You may have trouble getting full sheets of plywood down basement steps. You may have trouble getting finished furniture up those steps. I wouldn't recommend building a boat in a basement.

If your basement has moisture problems, that can lead to premature rust as well as moisture issues with wood working.