First is to check your actual vehicle for tow capacity and payload (possibly called CCC for your vehicle).
The calculations would be:
Tow capacity of Hyundai => GVWR of trailer (looking to stay at 80 percent or less of the tow capacity is a good idea).
Payload or CCC of Hyundai => weight of all passengers plus weight of driver over 150lbs plus weight of all gear put in or on the Hyundai plus 10-15 percent of the trailer GVWR (aka tongue weight).
If your trailer has a factory installed hitch, then the hitch weight should already be calculated into the weights. If you have a hitch installed, you need to subtract that weight from the available payload/CCC.
In addition, you have to determine what class receiver hitch you have/get. If you have a class 1 hitch, your trailer's tongue weight cannot exceed 200lbs. With a class 2 hitch, that is increased to 350lbs. It is highly unlikely you have a class 3 or greater hitch.
As mentioned, between those three factors, you are most likely looking at a teardrop or a folding trailer.
If you have kids and are looking to camp, I would recommend a softsided folding trailer (also known as a popup or tent trailer). If there is just one or two of you, you could look at a hardsided folding trailer like an a-liner. The a-liner is less work to set up and take down, but the interior space is more limiting than with a softsided.
1975 American Clipper RV with Dodge 360 (photo in profile)
1998 American Clipper Fold n Roll Folding Trailer
Both born in Morgan Hill, CA to Irv Perch (Daddy of the Aristocrat trailers)