Hi Mary, and welcome aboard.
Lots of great options for trailers, with most folk leaning towards what they own. I would suggest you do lots of reading on here, and see what folks have to say, then come back at us with all your questions.
Do you have a budget in mind? Are you looking for new or used?
You will also have to define your own needs for a trailer. Whether you want a full bath, full time bed, air conditioning
, and on, and on. Many of these questions, and others that come up along the way, will bear on your final decision.
Not sure what your current vehicle tow rating is, but if it is the vehicle you intend to use, you should check the manufactures load ratings, as this will help guide you with what you can pull. Do allow for the weight
of all the stuff loaded aboard too, with full-timing it will be a bit higher.
Most of all, have yourself some great fun with the decision process, as it is an exciting process finding and outfitting a new trailer, as I am sure you experienced with your previous purchases.
As far as cats go, HERE
is just one of many threads on travelling with them.