Welcome and congrats on your '97! The most important things are the roof and the tires. Your trailer should have a rubber roof, and these should be inspected a couple times a year. If the seams have never been resealed, you should consider doing that, especially before winter. The sealant used around all the edges, as well as around any of the things mounted to the roof (vents, TV antenna, etc.) will crack when it gets old and has lots of UV exposure. This will allow water in if not sealed up right away. Leaks on trailers are usually hidden until they are very severe. To apply new sealant, clean the surface, pick off any loose pieces of sealant, and then apply new Dicor self-leveling sealant over all of the old. You can buy this online or at just about any RV dealer.
The roof on your trailer isn't walkable as it is. You can put down some blankets/towels and some plywood to span the rafters, but the roof cannot support the weight of a person between them. That said, the roof should be relatively firm to the touch. If it feels like pushing on a balloon anywhere, that's a sign that you have a pretty bad leak. Still, seal it up so it doesn't get worse until you can deal with it.
Tires/bearings/brakes are also important, with the latter two likely ok already if your trailer is up to date on inspections. It's a good idea to replace the tires if they are at or over five years old, if you plan to do any highway towing with it. If a tire blows, which they like to do when they get old, it can damage siding, sewage drain pipe, underbelly material, and more. Make sure to also run the max sidewall pressure in your trailer tires. Their weight capacity severely reduces with lower pressure, which causes the tire to heat up more and can lead to a blow out.
2007 T-286SR Cherry/Granola, #6236, original owner, current mileage: 9467.8 (as of 5/26/19)
1997 T-2653 Blue Denim, #5471
1979 12 1/2' MC, Beige & Avocado, #4639
Past Sunlines: '97 T-2653 #5089, '94 T-2251, '86 T-1550, '94 T-2363, '98 T-270SR