Hi and welcome to the Forums.
You will find that there is always something to do on a 25 year old trailer. But, that being said, don't rip it apart right off. Go camping and see what works, what doesn't, what you like and don't.
New gaskets for the windows is a swell plan. Caulking as necessary involves some specialized products, you definitely don't want to be smearing silicone caulk on your new baby -- search the forums and you will get lots of ideas on what to use and how to use it.
The important thing is to enjoy the trailer between projects. A lot of folks go into "full rehab" mode and get discouraged because the fun quotient is low.
Get the running gear squared away (brakes,tires,bearings, balance) and go play!