Welcome, Gary! You’re in the right place for small and
light, however...
Not all are as
light as some sellers claim. In general I’d recommend a minimum tow rating of 2000/200# (trailer weight/tongue weight) for a 13’ egg trailer, 3500/350# for a 15-16’ trailer, and 5000/500# for a 17-19’ trailer. The higher you go, the fewer choices you have in the SUV class.
Those are broad generalizations, and of course some models are lighter or heavier than others of the same length. You can find more detailed
weight information in the “Trailer Weights in the Real World” thread in the General Chat section. Post #297 links to a handy spreadsheet. These are actual loaded weights, not manufacturer dry weights before options, fluids, or gear.
One important question to decide fairly early on is whether you require an onboard bathroom. Having one opens up more places you can stay (especially during the current pandemic), but they add a measure of cost,
weight, and complexity to the trailer. They can be toilet only, toilet and shower, or toilet with shower and sink. There are also alternatives to traditional flush toilets, including composting (separating) toilets that don't require plumbing and porta-potties that don't require a dedicated space.
Prepare for a significant hit to fuel mileage when towing, and the smaller the vehicle, the bigger the hit, other things equal; i.e., a 4 cylinder pulling a 13' trailer will take a bigger hit than a 6 cylinder pulling the same trailer, and the 6 cylinder will have more reserve power for climbing hills. Of course, when you unhitch, the advantage returns, so it's a trade-off. The curve changes when you introduce different engine technology, like hybrid, turbocharging, or diesel, but each comes with its own set of trade-offs.
Best wishes in your egg hunt! We’ve got a senior and a sophomore, so we’re also looking forward to some empty nest travel.