Legal Question in Real Estate Law in California

I'm not sure if you mean the best way to take title or the choice between a quitclaim or grant deed. The form of the deed doesn't impact your questions, though a grant deed is almost alway better than a quitclaim when retaining a part interest as your parents want to do for now. As for the form of taking title, Joint Tenants and Tenants in Common will both work. You should be more concerned about how you take title vis a vis your wife. I'm sure you will be married to the grave, but just in case that doesn't happen, you need to make sure you and your parents want her to have a share of the property even if she runs off with the circus, OR make sure she won't have an interest if you split up.

I don't know what "change my status" would be about. It may be a problem for the loan. Most loans have a "due on sale" clause that makes it either optional for the lender to call in the loan if title to the property changes (the nice version), or makes it an immediate default (the nasty version). So you will have to look at your parents' loan documents and see what they say. At the very least you will probably have to notify the lender and get their consent.

I don't know what the rules are about first-time home buyers. If the share of the property you will receive is worth more than $10,000.00, however, your parents will face a gift tax.