Where should I start repairing an older home with multiple problems?

The first thing you should do is get the roof repaired before any further damage is done. The next thing is to have the electrical updated to code to reduce chances of an electrical fire. Plumbing would be next, but make sure you have taken into consideration all that you plan to do to the home. For instance, you don't want to have the plumbing modified, then decide to remodel a bathroom or kitchen and have to redo what you've already done. Same with the electrical. Try to have a master plan before starting the work (after you get the roof fixed -- unless you're planning to add on). Having a master plan will help eliminate double work. There isn't much left of the government's incentives, but each state, including power companies, has different incentives. Make sure to do your research on those. Good luck!