What sample rate should I use on my ADC?
Depends on your specific application. First of all the guitar has a lot bigger frequency range than you indicate. While the fundamentals are in this range, the guitar has a lot of harmonics and in fact the bulk of the energy is in the harmonics, not the fundamental. So when you plug the low E string at 80 Hz, there is actually not that much energy at 80 Hz but way more at 160Hz, 240Hz, 320 Hz, etc. Same for the higher strings.

In the case it may be simplest to take an off the shelf audio ADC that operates at some standard rate (8000, 11025, 12000, 16000, 22050, 24000, 32000, 44100, 48000). The exact choice  depends on the requirements for your application. For ,say, a tuner, I'd do at least 16k.