I need an accuracy of 0.1% in the digital signal.
For that you need at least a 10-bit ADC. That means that you may get a quantization error of at most
1/2^n of your range, provided your signal fills the whole range of your ADC. However, this only accounts for the theorical minimum resolution you need. For real requirements, you need to account for noise, and that depends on a lot of stuff. To begin, you better use a 100Hz low-pass (antialiasing) filter (with the more stages, the better). That should take care of high-frequency noise. Then you should check the ADC's datasheet for non-linearity (which is usually considered as noise) and other internal error sources. Then you should check correct impedance matching (which when done incorrectly may increase noise). And since you are dealing with a very slow signal, you may also try Oversampling to get some additional bits from sampling at higher frequencies (software or hardware approaches). At higher rates you can also apply digital filters after sampling and before decimating.
How to determine the ADC parameters required?
Your most important parameters are resolution, sample-rate, noise and range. Assuming your "amplitude" means "peak amplitude", you need at least a 10V ADC to sample. Those are not common, so you'll probably need an attenuator or some other way to scale down your signal. Remember that those devices usually add more noise to the system (as does filters too) and that resistors add thermal noise too. Since you probably want to scale the signal a little more to avoid clipping and to allow for noise, you want to take into consideration how this affects your accuracy (your requirement is 0.1% of the signal, not of the ADC range).
Do I need to apply an offset first?
If your ADC is single-ended, you do need an offset. Adding an analog offset to the signal also adds its noise, so you should be careful selecting an analog reference which matches your requirements. Using a voltage divider from the power supply will probably get you into trouble because of noise (specially if using a switching regulator) and feedback. You most probably want to select a differential ADC to sample AC signals.
How is the process different than that for DC?
It is not. If you add an offset to a DC signal and use a single-ended ADC, you are actually sampling a DC signal, from which you'll have to subtract the offset afterwards. If you're using a differential ADC you have almost the same internals, except that you'll have a variable reference (which is part of the signal itself and usually avoids common mode effects) and the conversion allows for negative values.