We need to know what kind of band saw you plan to use and the size blade that saw can handle. For resawing, you need to use the widest blade the saw can be set up for. The blade needs to be sharp and be set up exactly 90* to the table. Using a fence is tricky because the saw may not track in a parallel line to the table. You need to run a line down the middle of a board and free hand resaw the board as carefully as you can for a few inches, then stop and see how the board lines up to the table. That is where you would set up the fence....but there is still no guarantee that the blade will track on that line all the way through the board if you have an inexpensive band saw.
One way to get around this is to use the end of a squared off board, set up on edge at the distance away from the blade that you want to split the board, instead of a full length fence. This will provide the guide for keeping the board centered, but allow you to move the board left and right on the end to keep the blade tracking down the center. One big thing you have to watch is internal blade wander. The blade can start curving inside the board, which you will not notice until the blade won't track anymore or the blade snaps or you finish the cut only to find that you have destroyed the board.
You will need all the thickness you can get. I doubt that you can get 3/8 boards from a 7/8 planed board. I would get the 4/4 rough boards and do a light pass on both sides just to knock off any high spots, then make the resaw cuts.