The order of problem solving for most designs comes down to a fairly simple order: Specify Requirements, Evaluate, Test, Refine, Optimize, Detail. (Repeating the last five steps in iteration). So, we need requirements. Unfortunately, requirements are tied somewhat into the design, so we've got even more iteration to do. Here's the order I'd recommend:
- Kinematics There's a reason you walk before you run. Solve your planned distance, time, velocity, acceleration, delta V, turn radius, etc. Consider your gravitational well you'll need to pull out of and the brakes you'll need to put yourself on once you get to your new one. This way you have an idea of your loads. Anything you can figure out that doesn't require knowing a particle's mass, such as velocity, time, and acceleration, are open here.
- Material Science Materials are a very real requirement, and this is where I'd start with for everything. This is for both the hull and the engine, as well as for the life support systems and everything else. Somehow we'll need to find materials that can hold everything up. We don't need to get into too much detail here, but we need to get a mass estimate and a basic size estimate to finalize the loads.
- Final Mass Estimate We then need to place and figure out the main components mass. Depending upon our constraints, we need to know the mass for passengers, life support, experiments, electrical, engines, etc. Finalizing this mass estimate will allow for sizing of the main components.
- Engine Sizing Once we finalize loading, we're in a better world to size the engine. We begin here using our existing materials science requirements and finalize a high specific impulse engine to meet out preliminary mass estimate.
- Main Component The hull, whose main purpose is to keep everything from falling apart during maneuvers, can't be finalized until we size the remainder of our components. Design them up based upon the duration of the trip (if that had to be changed during the engine sizing). If that changes the mass estimate, go back and redo the engine sizing.
- Hull Design Now with the final requirements in place, we need to test the hull. If it falls within our mass estimate, now we can move to optimization. Otherwise, back to recheck all of the assumptions that were based on the mass estimate.
- Optimize All along the way, and after you finish, optimize as much as you can. With more and more details in place, and with mass and other specifications in place, you can finalize a lot of details and find ways to optimize your design.