Let me back up for a moment, I realize that probably the first thing I should have done is given some advice on where/how to buy a vintage travel trailer. The adventure is a loopy one and if you are trailer shopping you might be thinking that you are going a little crazy so I'm here to tell you that you are not alone and to pass on some of my experience.
I'm a huge Craigslist fan and I use it to find everything from my kitchen stove to my furniture so of course I would also use this tool to find a vintage trailer (there is an RV section under the FOR SALE tab) One of the first things you will realize is that there is a huge variety of trailers depending on where you live and these will often have a huge variety of prices. I often remember seeing the same make and model of trailer being listed for vastly different prices. This becomes even more complicated since some people's definition of 'trailer is great shape' seems to be so vastly different from mine.
My advice is to watch the Craigslist ads closely for a few weeks to see what comes up in your area and a basic range of prices. It's helpful to be able to do word searches for things like 'vintage' or specific brands you might be looking for like 'Scotty' or 'Shasta' but the truth is that I found it best to just search through all of the ads to find out what is hidden. It's not unusual to see something like 'old trailer $200' with no other photo or description. Only after contacting the person will you find that it is a 1955 Shasta that has had one owner and has been stored in a garage for the last 50 years and is in mint condition. It is of course better to find the person who is just trying to dump an old trailer rather than the person that thinks of it as a valuable collectors item. RSS feeds are also very nice at this stage and a huge help if you know how to use them. Craigslist can be kind of hardcore and there are a lot of people out there who are probably much better at searching for treasures than you are so you have to learn pretty fast.
When you finally get around to going to see some of these trailers you will also be shocked to find out what bad shape many of them are in. People seem to forget to mention this often times in their ads and you will probably walk away from several trailers knowing you just wasted a chunk of time before you find the trailer you really love. Take this experience to get used to how trailers feel, the different lay outs and features that the different brands offer. Think of this stage as your education and don't be too eager to jump on anything, there are a lot of trailers out there and new ones are constantly popping up.
I quickly realized that the 1960's was the best era of vintage trailers for me. Old enough to look and feel cool, but young enough that I was seeing a lot less issues than I saw in some of the older trailers. This was about as much project as i wanted to take on.
Probably the most common problem you will run into is water leakage, this is a big problem and can cause a lot of structural problems so don't take it lightly. The most obvious places are the ceiling and the interior walls but search everywhere. The weak spots are anywhere that two panels meet so walk around the entire perimeter and push in the side looking for weak spots. Jump up and down on the floor and make sure you take some time to probe around underneath with a flashlight and a screwdriver looking for bad areas. Most travel trailers will have some problems so just know what your limits are.
The next most common issue might be rodents. Look for obvious signs such as rat poop, but I would suggest pulling out all of the drawers in the kitchen and looking in the cavities underneath. Someone might have cleaned up the trailer when the listed it for sale, but rarely to people think to look under drawers.
Use your imagination to look past things like bad curtains, ripped upholstery and torn flooring. These things might be a little expensive, but they are easy to replace and/fix.
Take time to learn about the different systems but in most old trailers these will need some work. Even if the propane all works I would probably want to replace all of the lines anyway. Know your limits and needs and take this time to figure out how much trailer you want. Start learning about different weights and how much you can tow behind your vehicle.
EBay is also another good tool to learn about different vintage travel trailers, but I would NEVER buy a trailer that I had not had a chance to comb over myself. There are just too many things that can go wrong.
Know your limits and think of every experience as a chance to learn. be prepared for some frustrations but know that your perfect trailer is out there waiting for you somewhere, you just need to find it.