I'm on my second travel trailer. My first was a 2008 Fleetwood Utah tent trailer, and my current a 2010 Keystone Gougar 322 QBS fifth wheel.
Here are some things that we found when trailer shopping both times.
Used could represent better value, as they have already taken a big depreciation hit. It seems after this big initial hit in depreciation, the value diminishes at quite a slow rate afterwards. This is especially the case if you have a minimally used unit. Our first we really lucked out, the previous owner used it only for a total of 6 nights on 4 trips the previous year to our purchase, when his wife told him they need something bigger so his mother in law could camp with them. Second trailer wasn't quite as unused, but it spent most of its life at a seasonal lot close to where it called home, only moving twice a year.
Versus new, you get a lot of "extras" thrown in by the previous owner as part of the deal. Wheel chocks, propane tanks, and on some units, spare tires and batteries are extra charges. And you benefit, if the previous owner was diligent, corrections made to the typically shoddy workmanship across the industry, plus add on gadgets (we have a solar panel, inverter and dual batteries on our current unit). But, it could very easily be the previous owner was not diligent, and they are getting rid of their headache that's now falling apart. An inspection is critical before purchase.
If you go new, you get the benefit of a warranty. But you may find it is in to the dealer a lot to correct build issues. My sister in law bought new, and her unit spent as much time at the dealer as it did camping in the first two years. Compared to our used units, we had no major issues requiring a shop, only things like replacing/tightening loose or missing screws on trim type items. Not to say all are like that, as I'm sure there are many out there that have no issues. But with careful used shopping, the previous owner would have dealt with all of the issues that manifest in the first couple of years.
In terms of what type of trailer and layout, know what your tow capacity is, and keep a healthy margin. Also look at many units, whether they be new or used, to get a feel for what's out there in terms of the models and floor plans that would suit your needs.
As far as makes and models go, this can be all over the place and can vary even just by the model year. My father in law bought a used Jayco fifth wheel, and it had no issues until recently, when replaced a bent axle, likely a result of bad roads anyway. But my sister in law's Jayco bumper pull, bought brand new was a regular in the service bays. Our Fleetwood tent trailer, we ended up with a "good year" for roofs, but they went through a lot of different roofs over the years, with some being notoriously bad. And though our Keystone is trouble free, we've heard of many more recent year models being plagued with problems. Google will also show you that some brands seem to crop up more than others for problems, but you will definitely find they all have some issues. Also, the overall design of some units may mean they could be more prone, or less prone to trailer sway. Google can help you there too. For a bumper pull, look into a good weight distribution hitch with sway control. And with any type, if you don't have an integrated brake controller, pick a quality unit. Tekonsha Prodigy and P3 are recognized as good models, but there are also other good ones out there.
Not many will do this when shopping, but on our second go around, tire upgradability was something I looked at, preferring units that had 16" wheels, versus 15", as that opened up many more replacement tire options. Read about the ST China bombs, and you will quickly see why tires were a concern for me. My own research, including help from CapriRacer in the tire sub forum here at BITOG, was my guidance to choosing suitable LT replacement tires. (As a side note, there is a whole can of worms you can open with ST versus LT tires, with many in the ST camp offering a lot of admonishing, but can't really offer any concrete reasons why ST is better than LT in their view).