Ok Hold your horses everyone.
1. Stick with sRGB, that's a good decision. AdobeRGB has a larger gamut yes, but you know you need to be able to print that larger gamut and capture that larger gamut. For most of the visible work unless you use a polariser and bump up the saturation afterwards your image will fall within the sRGB gamut, and the only exception to that rule is orange sunsets which tend towards yellow when constrained to sRGB. AdobeRGB is *better* if and only if you have a killer scene with some ludicrous colours, and you print on something like an 8 colour printer, or go to a lab that'll charge you a fancy $20 per small print. If you don't do this you won't notice any benefit at all from AdobeRGB. In fact all you get is the disaster headaches from having to remember to do colour conversions and be aware which colour space your images are in before you upload them to the net or send them to your friends who may just see it as wrong. You bypass all these issues with sRGB, since it's the standard.
TN panels can display the full sRGB gamut. The 6bit issue comes into branding. It can't display every colour within the gamut smoothly from black to the most saturated red green or blue, but it will most likely display the full gamut (i.e. the chromaticity of the red should be the same as any other screen for the sRGB value of (255,0,0))
Photoshop can draw middle grey any colour value that falls outside the set colour gamut. This is called softproofing. Read this:
http://homepage.mac.com/ilyons/pdf/ps6_sp.pdf
2. You are calibrating a colour profile but not the one you are talking to. There's 3 types. Input profiles, Working profiles, and Output profiles.
Input profiles are what is used to convert say Scanner data or Camera sensor data into Working profiles.
Working profiles are the range of values the current file has. It defines that the value of RGB(128,64,64) will have a certain chromaticity. For instance sRGB(128,64,64) = AdobeRGB(114,66,66) = ProPhotoRGB(85,57,50). All of these have different values in the file, but all of them are the same colour to a colour aware program.
Finally you have output profiles. This is what you are calibrating. A non-colour aware program will say ok you have a value that we assume is sRGB in the file, lets send it to the screen and assume the screen is sRGB. Photoshop will open the file, look at the working profile, load the colour profile for your display, and send to your display driver and adjusted version so that what is in your display profile accurately reflects what is in the file. The display profile is created by your calibration unit. The same applies to the printer which also has a different output profile, except this conversion is often enough handled by the printer driver.
3. The calibration utility that comes with OSX I believe is one that uses your perception to adjust settings. I'm not sure on the details. If that is the case then it's crap. Don't worry though pretty much any calibrator you buy should have some software for OSX. The Huey as recommended above is a good choice. I own an iOne Display 2 and I will wholeheartedly recommend that one. Another choice is the Spyder 3. Shop around if you want, but essentially they all do the same thing.