Liz,
I wouldn't think we'd generally be in a good position to judge what skills you should pick up. I'd suggest doing the mental exercise of running your protagonist/"heroine" through the sort of scenarios you were talking about, or others, and see what skills seem appropriate.
I've been driving (ad nauseum) for decades, but on this side of the pond that's sort of taken for granted. I can (and do, by preference) drive a manual/stick shift, but they're getting harder to come by here- might not be that much survival value in it.
I can also sail a boat, navigate tolerably well, and ride a horse- but I've often thought that I really should be able to ride a motorcycle as well. I'm completely at home backpacking, and doing map-and-compass work where there are no trails, but I couldn't land an airplane. I have fair experience with shooting, a few martial arts, even fencing, but, to my shame, the only Morse code I know is S-O-S. My command of other languages is abysmal, and I don't even have a passport. Even though I "batched it" for some years, my cooking skills are primitive at best, with the exception of maybe two or three simple dishes- I have baked decent bread a few times, but it took longer to clean up the kitchen afterwards than it took to grow the wheat. When I had to eat my own cooking I ended up a lot thinner. Speaking of which, my attempts at gardening have been about 25 percent successful- as a subsistance farmer, there's little doubt I'd starve. I've never plowed- er, ploughed, a field, or practiced animal husbandry much beyond feeding the cat. I can sew by hand, but not by machine. My one attempt at finger-weaving was an embarrassment, and I've never spun yarn or thread, or laid rope, for that matter. I've done blacksmithing and leatherwork, but I'm just now learning a little plumbing. I've never been a parent, was pretty much brought up as an only child, and would have only the vaguest idea how to take care of kids, much less infants, and far less teach them anything. I worked as a mechanic of sorts, and can do a fair amount of mechanical repair, but I have no machine-shop experience, or carpentry, or welding. I can start a fire with (real) flint and steel, but I'm not comfortable with a chainsaw- though I have used one.
And so it goes. Your list is going to be very much your own. List your strengths, and I'm sure the gaps will come to mind.