Obviously you need a board flattener and a board strecher ( it is an old shop joke on newbies) . It looks like a very interesting situation and a lot on choices would be dependent upon the exact nature of the project. A small project such as a small box or a project that uses small parts such as an end table would be much less problematic that a project requiring large pieces such as a larger table top. If the project requires keeping the weathered surfaces then maybe the splits, cupping and twisting can be incorporated into the design. I would tend to try and use the worst pieces for the smaller parts to minimize the overall amount of cup. twist. and bowing that must be dealt with. Rough cut the pieces first. Most heavily weathered boards will have lots of minor cracking throughout the boards but it usually becomes more of a finishing issue than a structural one. Boards normally have a lot of hidden cracks on the ends so I would avoid using the ends when possible. Cupping can be dealt with as you suggest and I have also seen kerfs cut on the concave sides partway through the board and battens used to pull the board flatter, maintaining the visible surface grain continuity. One of the great things about traditional woodworking is the it gives you more of an opportunity to use the unique features of individual boards. It would really help to know more about your project.
Keep us posted I would love to see the finished project.