Carl, Fitz makes some excellent points; a compound miter saw, in order to cut very wide material, needs to be a SLIDE compound miter - these are available from DeWalt, Makita, and a few other manufacturers, but a 12" version will run you at least $600 new.
To my knowledge, there is no compound miter saw at ANY price that will let you rip even a 2x4, much less a 4x8 sheet of plywood - but for most of the cuts you would do in building a studio, the compound will do a good job.
As to "skil" saws, in the right hands they can do nearly as precision work as a table saw for normal cuts; Fitz mentioned one of the main tricks to accomplishing this. For narrower cuts that still need precision, I have a few cam-action "clamps" that can also be used as an edge guide; these speed things up for doing repetitive "guided" cuts with a skil saw, but are not cheap; seems like I paid around $25 or so for each one, depending on length. I have 2 that span just over 4 feet, and two 3 footers. These have come in handy for a LOT of things, glad I bought 'em -
http://woodbutcher.net/images/normstools/tru-grip.htm
In the pic, that wide black thing in the middle is the rear cleat - you squeeze the wide parts to release and re-position the cleat, the opposing cleat is on a lever-actuated cam; lift the lever, slide the rear cleat up til it's snug, then flip down the lever. There are 2 or 3 "stops" in the cam position for differing degrees of tightness. Works really well and quick, either as a clamp or as a straight-edge guide for a saw or router (even for a straight cut with a jig saw, if you don't push it too hard)
As to skil saws; if you're pretty strong, and want the best accuracy for cuts, get the REAL worm-drive skil saw - it's heavy, which is both a plus and a minus - the plus is, it doesn't wander when you go through grain with the blade; the minus; this sucker is HEAVY, and at the end of the day you'll know you used it. Cost is around $140 if I remember correctly.
For that reason, I recently bought a Porter Cable "sidewinder" type framing saw, with the blade on the left - it's magnesium and carbon fiber, weighs a little over HALF what the Skil weighs, and is great for quick cuts without wearing you out; however, without a FIRM grip it WILL wander when you hit varying density grain structure in dimensional lumber; because of this, for precision I don't recommend it. Cost of this saw was right at $100 @ Home Depot last year.
IF you need to do much demolition first, a good recip saw will come in very handy; just don't cut through any power wiring, it's very exciting but not good for weak hearts

- for this type saw, I would ONLY recommend a fully counterbalanced version; I have the Milwaukee SUPER Sawzall, and it is WELL worth the extra $$ over their standard model or any other I've seen. Has more power, longer stroke, and NO VIBRATION so you can actuall cut where you WANTED to, instead of where the damn saw JUMPED to...
If you're "cutting in" electrical boxes or removing just one layer of flooring, another handy tool is the "Roto-zip" - basically a miniature router with special bits that work as a depth-controlled saw - you can get bits for wood, drywall, ceramic tile, etc - this thing makes a serious mess when cutting drywall, so makes an even stronger case for a good shop vac. The good thing; you can cut out sections of drywall without worring where your power (or plumbing) is running, because you can set the bit depth to exactly the thickness of the material you're removing. You can also get much closer to corners/walls than anything else but the Sawzall.
I could go on all day on tools, but this along with Fitz' help should give you an idea of what you need... Steve