I think - AGM. For 500W it's 4*100 AH @12V, or at least 4*90.
Their plans to put 8 (!!) GC in a storage compartment of travel trailer sound scary. Sliding tray is one pain, reinforcing the bottom is another. Somebody on that list of projects did this - welded an extra I-beam underneath the frame. And then yet another pain - literally - acid fumes from 8 batteries in the trailer.
With power hungry (=current heavy) items like MW, coffee maker, toaster etc (in other words, things that you could live without, if it's just one week), they would need 4 GC or 12V equivalent in AH. With only 2 GC, the current will be high per cell, and 250 AH leave zero margin for when it rains.
Then again, their generator plans are not clear, and neither is energy consumption pattern, i.e. all those not mentioned "other small electrical items". Those that they did mention - TV, laptop etc - don't consume much. 2 GC with 500W panel could work IF there are no high-current items and/or there is a genny for backup. And then there are plans of adding more panel wattage - how much more? Too many variables to suggest anything...