if I want to purchase an Apple Watch through say at&t do I have to do it on the same account as my phone or can I open a new account and have just an Apple Watch on it?
I believe that it has to be on the same account that you are using your iPhone on, because the LTE version of the Apple watch uses number share with your Iphone. You will have a different number for your watch but it is for billing purposes only.
@mrwalleyeman is correct. Your LTE watch and your paired iPhone must be on the same post paid billing account with AT&T and the other Big 3 carriers here in the US. Carrier's don't want to bother with a watch only plan, not worth the overhead costs for a $10-$16 account.