This has been discussed ad nauseum. Have you searched the forum?
For practical purposes, 8-bit is what you're used to, is faster than 32-processing, is more predictable, and is more stable. Almost all of the formats you'd render to are 8-bit formats.
32-bit processing does a few things for you. It converts your 8-bit/channel media into 32-bit/channel media (in RAM), does all its calculations, and then converts it back down to whatever your output format is (generally 8-bit, but you also have the option of writing 10bit/channel files now, which I suppose is useful if you are outputting to high-end tape formats).
Doing your processing in 32-bit mode should give you cleaner effect and transition processing and slightly cleaner results even if the final output is still 8-bits/channel. Whether the trade-off in slower render times and premature balding is worth it is up for debate, I think, but if you need to output to a 10-bit codec then you should use 32-bit processing.
32-bit processing also gives you two gamma choices. Glenn Chan has said that 2.222 is the safer and more predictable bet. The 1.000 linear mode gives you different results in some modes and you might like that mode, but you really need to do tests.
You can switch your project between the modes but certain media formats react in different ways so you need to pay close attention to black levels. If you're going to switch back and forth I'd probably recommend you do it before you ever render anything since the modes can affect how things will render.
Search the forum. Glenn has published quite a bit of useful info on his web site but there's a lot to absorb. I suspect that Vegas will change it's handling of some issues with 32-bit processing as patches get released down the road.
In the 2.222 and 1.000 you can do the same things by manually converting values to the other color space. I'd recommend working in 2.222 since it's harder to get wacky results and to run into unintuitive behaviour. e.g. in 1.000, most filter presets don't work / are inappropriate.