If I were in your position I would get the general GRE out of the way early and leave plenty of time to focus on the physics GRE. I think there is a lot you can do to prepare for the general GRE but you can do it with the coursework you already have. For the general GRE I suggest you pick up a book that outlines some basic strategies for taking the general GRE (i.e. Kaplan, Princeton Review, Barron’s, etc.) and work on your test taking skills and strategies and take a bunch practice tests under actual conditions. I think it helps to work on your timing, stamina, avoiding careless errors, and getting very familiar with every type of question you might see on the exam day. If you have extra time on your hands then you might also want to work on building your vocabulary and improving your reading comprehension and speed (these skills will also come in handy later in life so it is not wasted effort).
The physics GRE is a bit different since during the next year or two you will be learning lots of material that you will need for the physics GRE. You almost have to put off taking physics GRE off until you need to take it for your grad school applications (but you still can start preparing for it). You will have enough to juggle while you are preparing for the physics GRE and you don’t want to be worrying about analogies and silly reading comprehension stories while you are in full swing in your preparations for the physics GRE. I remember some people actually took both the general GRE and physics GRE on the same day. I’m sure most everybody that ever did this would strongly advise against it.
Note: I called a school that did not accept me and asked what the weaknesses in my application were. The first words out of their mouth was “Hmm lets see what did you get on the physics GRE” and then I think they went to coursework and I don’t think the general GRE was even brought up in the conversation. The point of saying this is that the physics GRE is looked at and so are grades. I believe the general GRE is looked as well but I don’t think you want to let your grades or physics GRE suffer because you want to be able to solve some problem involving angles in a triangle within 20 seconds or less with 0% chance for error.
Note: Most people study quite a bit the summer before they take the physics GRE. A good portion of their preparation effort involves reviewing (or actually understanding for the first time) their freshman and sophomore level coursework. So there is a lot you can do right now to help you prepare for the physics GRE.