DC, AC,, battery, asynchronous?

Hi all,

Planning on getting a new turntable at some not-too-distant point in the future, and so am obsessing and researching. One issue over which there is much chatter is the sort of power supply. Is someone out there willing to give me primer on this issue? What are the costs and benefits, in principle and audibly, of A/C (as in Rega -- a P25?), D/C with a transformer (as Michell offers -- thinging about a Technodek or used Gyro), D/C from battery (probably out of my price range, at least at first)? And what is the deal with synchronous/asynchonous power (if that's even a coherent way top put the question)? I know at least one frequent poster here thinks this is a central distinction. Enlighten me. If it matters, amp is a Naim Nait 3 with flat cap. Current deck: Planar 2, RB-250, Dynavector 10x5.