Hi Mary,
There are individuals in the building trades who (for a fee) will inspect your new rental and advise you on whether to buy/repair or move. I have never needed their services so the fees are unknown. You might start at your county building dept.(or your local equivalent) for ideas on who to contact. With a few years of Rough, and Finish, Carpentry work behind me, your description of the whole house shaking by just shutting the door makes me nervous. It sounds to me that you should spend enough money to make the house safe and weather tight and save the rest for a better place. If you REALLY like the place, go ahead and spend the money on what you have. Another option, where I live, is to tear down the entire house except for the soundest wall. Then rebuild a new house just like the original. This way you are remodeling an existing home, not building a new one. Then sometime later, replace that last wall. If you tear down the entire house first, legally you are building a new house from scratch. Much better the first way, financially.
I am sure that, with the knowledge base we have in this group, there are people who can give you advice as good as, or better than, I can. Consider how quake-prone your area is too.
Good luck,
Byron