I moved from the US (MI) to France and then Spain, but am living with my parents while looking for jobs here, so a bit of a different situation regarding most of your questions, but I’ve helped some people move across the US so I have some experience there! If you have a car with a hitch, you can fairly cheaply rent a moving trailer from UHaul or something similar. That should apply to the US (and Canada I would think). Renting their vans tends to be quite expensive, and shipping is outrageous now, so that’s probably your best bet. Generally, if it will cost more to transport it then it would cost to replace it, it isn’t worth taking with you (this applies more towards shipping).
Haven’t been on the west coast of the US much, so I have no idea what or where to recommend for that, but I know it can be very expensive. I’ve heard Northern California can be relatively affordable, but no experience there. I doubt this was of much help, but I wish you the best in reaching a place where you’ll be happier!