While jrista's older answer that's been linked to gives a lot of background, for most people who just care about producing good results, things can be simplified a lot. There are basically two possibilities that (IMO) make much sense. For lack of a better term, I'd call them the "high end" and "low end" options1.
High end: ProPhoto RGB working space, 16 bits per channel.
Low end: AdobeRGB working space, 8 bits per channel.
In either case, you want to profile your monitor. IMO, if you care about color fidelity at all, it's worth getting and using a colorimeter. If you want to go for the really low-end version, Adobe includes a calibration program with Ps (and probably with Lightroom and such as well). I suppose if you really refuse to use a colorimeter, it's better than nothing -- though only a little bit, to be honest.
From there, you can convert to sRGB (for example) when you're publishing something to the web or getting a print from Walgreens (or whatever). In a fully color managed work flow (e.g., a pro-level printer or doing your own prints) should go directly from your working space to the profile for the printer/paper combo being used.
Just in case that wasn't clear: sRGB (somewhat like JPEG) should only be used as an output format, and even then only in situations where the destination is unknown and uncontrolled. It's never really a good choice -- but when/if the destination (probably) doesn't manage color at all, it's the least of the available evils.
1Trying to mix these to get a mid-way point doesn't really work well. AdobeRGB with 16 bits per channel doubles file sizes without improving quality. ProPhoto RGB with 8 bits per channel will frequently result in visible "banding".