Hi Tiffany, and welcome to Allnurses!
It sounds like you've stabilized and resolved your depression issues, and are ready to roll. Good for you! I know it's tough being a nurse with MI (I'm Bipolar 1 with rapid cycling) and trying to rebuild a career. It can be done, though, as long as you're stable and adhering to your treatment plan.
However, I'm pretty sure that your state BON will require a formal refresher course before allowing you to work. Things change so fast in our world that self-study using books that are more than a year or two old won't suffice, and of course there is no substitute for the hands-on clinicals where you'll be working with real patients.
You may have to borrow money or get a short-term loan to finance the course, but you really should do whatever it takes because it'll be worth it in the long run. It will also provide a safe environment which will help you confirm that you are truly ready to resume your career.
As for your other questions, I echo what MrChicagoRN said above: take as many CEUs as you can, and consider dipping your toe in the water first before committing to a full-time job. I'll be honest with you, full-time is very hard on a nurse with MI and you'd probably be well off with 32 hours/week, or even less if you can afford it. (You probably want health insurance benefits, but many companies offer them at 30 hours/week and up.) Home health sounds like a good choice, although getting a HH job may depend on how much experience you have.
You could also try working PRN at first as an admissions nurse for a long-term care facility (my current job). You get the 1:1 with the patient during the process (that's my favorite part
), plus you serve as a resource for both him/her and the family as they get settled in. You also are no longer responsible for them once the process is completed and you hand them off to the charge nurse, which is a HUGE advantage if working with lots of patients at once makes you nervous and overstimulated.
As for your resume, I think 'caring for an ill family member' would be a better way to explain the gap in employment. It's not really any of their business anyway, but they often ask this question and you don't want to make it look like YOU were the one you were taking care of. Discrimination is still alive and well, unfortunately, and if you give them even a hint that you needed a 'sabbatical', they probably won't hire you.
Wishing you the best of luck. I hope you'll keep us posted on your progress.