Hi Robin and welcome to the forum! I used to live in the valley so I know what you've been up against.
I'm sure some of our members will chime in soon with suggestions on the best way to approach FT on a budget. Being economical hasn't been my area of expertise.
You can use the search feature to find previous discussions on the topic and there are a lot of trade offs to be made when picking a rig. My initial reaction is to suggest a Class C and maybe a small tow car but that just might break the bank and complicate your learning curve so I'll let others who have been there and done that comment further.
We've been full timing with our three dogs and our biggest concern about leaving them alone in the coach is the possibility of a power failure at the camp ground on a hot day. Just something to keep in mind.
Best of luck to you.