Speaking from experience, I would start at the hospital. Home health/hospice require very independent thinking and sometimes crisis situations occur.
Getting your "feet wet" in the hospital for a year or so will help you out tremendously. Also, while you are working in the hospital, and a crisis occurs/pt crashes, there is always someone down the hall to help you.
I did my one year med/surg prior to home hospice. I would have been SUNK if not for that hospital experience. Now I am more confident and comfortable w my skills.
I've been doing home hospice for 3 years now.
Congrats on your new position; I hear they are hard to come by these days.