Build a basement studio..?

I don't know how much of a risk your basement has of taking on water, but I've had 2 different ones do that under two completely different scenarios. I developed a rule of keeping all of my electrical connections mid-wall to ceiling. Nothing on the floor.
 
Good luck with the space. Gotta be really exciting.
 
Don't want to be a spoilsport, but I've worked around some serious AC (like direct lines into Commonwealth Edison generators driving 480VDC/5000ADC 12-phase power supplies feeding 70 milliohm magnets)...and it scares the crap out of me.

You will probably want to put up drywall and insulation even on your 3 concrete walls.  It is easier to hand things on drywall.  My advice is to make the space "inviting" so that you want to spend time down there.  If its cinder block/poured concrete walls and a concrete floor it might feel a bit like a cave.

some good advice, I hope I don't contradict too much of it<G>. And a lot of this is guesswork, as you did skimp a bit on the details.

Use the existing block walls to the extent that you can. They are already pretty massive, and if there is earth on the other side of them then very little noise will escape through that path.
 
And don't sweat the floor. Yes, floors can transmit sound, and isolating the floor is tempting, but if it is poured concrete on earth then it is, again, already pretty massive, not a lot of sound escaping (or entering) through the floor!

Do not attach your new ceiling directly to the joists, even z-channel will transmit sound. If at all possible build a new structure and let the new ceiling be isolated. This is very often the most problematic boundary.
 
If you have plumbing, radon piping, or any other noise maker put a wall between you and the pipes. A massive wall that is as air tight as you can make it. If that is not practical then wrap them with lead loaded vinyl.

As Bit mentioned, the downside of isolation is that sound can't escape (which was the goal). Be prepared to treat room modes, they will almost certainly be a problem separate from the rest.
 
Think through any and all power, signal  and HVAC paths. Once you build the room you do not want to revisit these.
 
Consider an isolation transformer feeding a separately derived sub-panel. This is one area where an awful lot of folks seem to skimp. Sometimes it is no big deal. Sometimes it is a big deal. Better to avoid it all together.
 
Rod Gervais' book is good, really good from the perspective of the various trades. It is, in my humble(?) opinion weak in other areas. Especially room treatments. I'd suggest any of the books by Philip Newell, and if you can find a copy Jeff Cooper's book (which is a little bit dated, but still quite useful.)
 
Truthfully, if you are going to DIY (and I think that is a great idea) you are going to need to do some serious reading.

With an "unlimited budget" I think I'd by my own house and build one in there.

I would second what Jim said. I know you suggested an unlimited budget but this doesn't seem to line up with your situation right now.  It can be really difficult to completely eliminate noise from an old house or any house basement for that matter. The best ways to tackle the problems require a decent investment even for a small studio.
 
Obviously  ITB recording and headphones are the best portable answer if this is only temporary or transitional. They make special sound deadening blankets you could hang down there or even run of the mill blankets can help to some extent. The concrete floor acts like a hard surface sound reflector so covering it with a thick rug will at least stop the higher frequencies. Without a larger investment though it isn't ideal.
If I were faced with your dilemma I would likely use a laptop and headphones for a basic mix. You can mix upstairs where it's comfy or while waiting for classes at university. Then take it to another space for a better mix using monitors. You probably have friends with a place they wouldn't mind lending for a little while. Does your college have a sound studio? Many do and this might be something to look into.
When I'm recording I notify my wife or I wait until no one is home and much of the time it's late at night when others are in bed. Being in a basement with people  walking overhead can be a nightmare for recording.
Either do it right or don't do it. I would vote for the latter and more portable setup instead. Anything else is a compromise.