Very good questions! As with everything, they all have their pros and cons. I'll list a few for you to consider. There are many points to look at, but these are a few of the basics.
Cut-off wheels:
Pros:
Very easy to use
Able to be pretty precise
No expensive equipment required
Wheels can be found pretty cheap
Cons:
Slow
Noisy
Not good for cutting curves or short lines
Really slow on thicker metals
Oxy/acetylene:
Pros:
Relatively low cost
Multi-use:
--Can weld, even very thin metal
--Can heat metal for bending, shaping, freeing stuck bolts, etc.
No extra machinery needed to use it
Can cut any curve or shape and also holes
Cons:
Requires a little more skill to get nice clean cuts
It does put more heat into your material
Higher fire hazard
Somewhat expensive to get set up (with good regulators and tips. DON'T GET CHEAP HARBOR FREIGHT TYPES!!! )
Plasma:
Pros:
They're AWESOME!!!!
Faster cutting
Less heat build-up in material due to faster cutting
Very clean precise cuts
Cut any curve, shape, or hole
Able to cut multiple metals, steel, aluminum, stainless, copper, brass, etc.
Lower fire hazard than Oxy/Acetylene
Cons:
Most expensive option
High volume air compressor needed
Air needs to be VERY clean and dry, so usually need an air filter/dryer
220V circuit needed, curcuit amps depend on size of unit
Single purpose tool: only good for cutting
If you have any questions ask away. I have both oxy/acet and plasma, as well as a horizontal bandsaw. And I still use cutoff wheels as well. Also, consider what you are cutting. If you are mostly cutting tubing, channel, angle, etc, then some kind of saw will be far superior and more useful than either kind of torch. There are "hot cut" chop saws that use abrasive wheels, "cold cut" or "dry cut" chop saws that use carbide toothed blades, and then there are horizontal band saws. I like my band saw a lot because I can set my material up in it and walk away from it while it is cutting. With chop saws you have to cut each cut yourself. It really all comes down to exactly what you are wanting to accomplish. If you have questions about the different kinds of saws, let me know.