So gentlemen...

Coming as a 21y.o. near-college student living at home, let's propose that I had a good amount of studio gear, an unfinished basement in which said gear is located, an "unlimited budget", and the desire to put together a sweet basement studio for mixing recordings and doing tracking.

I'd want to mute the majority of external sound (I get some bad footsteps from upstairs, there's a wide PVC pipe connecting directly to a toilet in my current space, and the stairs are to my back right now so any sound near them makes its way down here.), as well as getting to where they don't hear ME too much upstairs and I can feel free to play as loud as I need to at any time during the day.

I'm considering trying to get something serious built, and currently my two options would be between either a 11'x7' space that I'm using right now, which is located basically at the middle of the basement against a wall with open sides and back (no isolation), or a ~11'x 5' space squeezed in a small sort of "annex" area in the basement with just one open side and 3 walls.

The smaller space would be much cheaper because I'd only need to construct one full wall, wouldn't need as much insulation in the ceiling, but it's also pretty tiny and narrow compared to the other spot (I'm measuring by eye). With my current larger space, It's nice because I can reach everything around me, but all the noise issues I mentioned are still there AND I can't really see myself having an entire new room constructed in the middle of the basement.

So I guess my question is, based on these few statements, what would I need in order to fulfill this dream of making a proper basement studio? I'm talkin' not only how to get the area of the basement finished, I mean also as far as building restrictions, what's safe, what's desirable as far as a home studio goes, etc etc.

Thanks guys!

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.

Pick up a copy of Rod Gervais' book Home Recording Studio: Build it Like the Pros. I have several books on studio construction, and while some of them are deeper technically, this is the only one coming from someone in the building trades. There is a section devoted to decoupling from the floor above you that you'll find helpful.
 
Basements are great for sound isolation (unless you're on a busy street with lots of truck traffic). But that high isolation is also the source of most problems in basements: inside sound has nowhere to go so it just bounces around in there, exacerbating room resonances. Plan on putting in as much fiberglass as you can fit in there, which special attention to corners.

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.

You're getting some good advice so far. I can add my experience about the plumbing sounds.
 
I started with a 12x12 ft basement room, 1.5 ft lower than the rest of the basement.  I used soundproofing insulation and two layers of thick drywall with Green Glue between them. I attached the ceiling drywall with channels and clips. I treated the PVC waste plumbing from the kitchen above with mass-loaded vinyl, and that turned out to be effective. Less effective was the treatment for the copper supply plumbing, so I can still hear the water running through it.
 
There are two glass-block windows, and I added two more layers of window glass in front of them, so I hear almost nothing from outside.
 
I didn't do anything to treat the HVAC vents, and that's the main leak from the studio to the house. Plus, even with all the drywall, I can sometimes still hear footsteps above.
 
As far as flooding, the studio includes a small closet with a sump pump with a battery backup. During heavy rains, the pump handles a lot of water, and I wouldn't want to record then. Another small closet has the radon-removal PVC pipe in the back. Before treatment, it hissed. Now I never hear it.

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.

I used these http://kineticsnoise.com/arch/isomax.html on my basement ceiling with 2 layers of 5/8" drywall and couldn't be happier with the results.
 
Rocky

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

If the space is in the parent/s home, that's somewhat tough.
If/when you move out, your studio space won't be moving with you.
Thus, I'd be careful with the amount you're planning to spend (unless you have unlimited resources).  
You may do better thinking about "less-permanent" things that would help.
ie:  Thick carpet, framing and enclosing pluming, walling-off furnace and/or utility area

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.