Welcome!!!
In regards to looking for the right tt for your family, the best thing to do is look at as many as possible, and spend some time if the owners don't mind inside. You can make sure the trailer is big enough for those rainy days when being outside isn't possible. If the model has a "parents bed" (full or queen) and a bunk bed set with at least dinette (and possibly a couch) it saves making the dinette or couch into a bed every night. BUT a bunkhouse is usually a little more in demand, so possible a higher price (at least when we have shopped! Lol).
Make sure everything works on both electric and gas (if the appliance has that option). Look for water stains and soft spots in the floor, walls, and ceiling. Even in the (pass through) storage areas.... Check the propane tanks date code if an older trailer. May need to be re-certified... Also check the rubber propane hoses!!!
Check the tires!!!! Just because they look ok, doesn't mean they are!!! Look for a four digit number indicating the week and year the tires were made: 1413- made the 14th week of 2013.... Plan on needing new tires when you start looking. The average tire life is 3-5yrs depending on how they were taken care of.... Not knowing the previous history: ran with low air pressure, extreme speeds, etc, you should plan on replacing the tires unless the owner gives you the right impression.
While you are currently looking at a smaller tt, don't get caught up in the infamous tow ratings of the 1500/150's!!! They will run out of payload before reaching their max tow rating. There is a yellow sticker in the drivers door jamb of all cars/trucks since '06 (or so). It will state: "All passengers and cargo not to exceed XXXXlbs".... Any passengers in the tv, any accessories added: truck topper/step bars/mud flaps/etc, all cargo in the bed: coolers/firewood/bikes/etc, the wdh, AND the tt tw (travel trailer tongue weight) should be below that yellow sticker payload amount....
Follow my signature links to learn about the wdh. You will need to adjust it to your truck once you load the tt up for a trip.
If the wdh is not included with the trailer, look for a good, integrated sway control model. The Reese Dual Cam, Reese SC, and the Equal-I-Zer 4 way system are all very good for the money!!!
Good luck!!!