Old house, crazy town in the basement in regards to wiring. I'd like to clean it up a little, at least visually - happy to get contractor out if needed - but not sure what to ask for. So what would be my options for for this? Vast majority of wiring is attached to joists with electrical staples.
I cleaned up the wires in my basement by removing the ones that were no longer being used for anything--old phone wires, TV cables, doorbells, even a security system that had been removed years ago. This removed about half the wires I had. It looks like some of yours could be similar. Then, if you have some wires that aren't stapled up nicely and are droopy, you can fasten them to well-secured wires with cable ties.
The sloppiest wires in your picture (the ones hanging down low) look like coaxial cable lines and cat 5 networking wires. Not sure how neat you want the end result to be, but you could certainly clean up the mounting of those low voltage wires. If they are going underneath joists, make small holes in the center of the joist to route them through. This won't cost you anything (if you do it) or much (if you hire a handyman).