Hi Flirty - I clicked on this to make the short answer (after reading too many planted questions) then I read the whole question and reached for my copy of The Practical Handyman
Apparently, you do the panels first; then the the vertical pieces in the middle (called muntings!!) then the horizontal "rails" (top, middle and bottom); lastly, the "stiles" (the verticals, left and right.) All of these should be painted from top to bottom. Remember, preperation is everything; you'll only get a good result if you remove all the old paint, or at least rub it down - otherwise just spray it with a couple of cans from Halfords!