Go with a dropped ceiling. Make sure the wires are good and are safe, first. You need to have access to all those wires, in case of future problems, so a drop ceiling is a lot more practical, and less expensive than having to tear down the ceiling when you need to access.

I don’t know your building codes but where I reside those would be judged a fire hazard. Have them inspected for your family’s safety and corrected if so advised. Depending on how recently you purchased the previous owner or home inspector may have some responsibility.

That tangle of unsupported wiring and open junction box(es) is against all electrical Codes and dangerous.

It's an unpleasant job. But I'd remove the drywall, which will likely expose more hazardous electrical shortcuts, and have the wiring done correctly. (On a new build, my electrical contractor was fined $1,000 for running one 3/10 cable the way yours is--$500 for the first inspection, another $500 when it wasn't corrected on re-inspection.)

After that, you can decide on a dropped ceiling or new drywall.

Kind of looks like what my parents had. After 50 years of my dad's diy electrical work in the basement rooms (including a bedroom) my mom hired a electrician to redo what dad did. Took about three days for one guy to do it all. Some stuff was done with extension cords. They did keep a lot of the metal conduit electrical wires used to be run through and just ran the stuff through them when they could.

Was there a suspended ceiling covering a drywall ceiling? That would make ceilings really low.

As it is, your suspended ceiling is 6'-8"ish. Minimum habitable space height is 7'-0" (6'-4" under beams). Remove the drywall and put it into the joist spaces, no furring, new drywall tight to joists. All the non-metallic cabling needed support anyway, not just draped onto the suspended ceiling, it looks like with firetaped drywall then adding a suspended ceiling that this may have been the original garage or something like that.