You will not have any issue with the trailer swaying if you get the right hitch. You want to get one with load leveling and sway control. With the correct hitch and a truck that can easily pull the weight, you will be fine. Do not get a trailer that is close to the maximum the truck can pull. You also do not want to use the empty weight of the trailer - use the weight of the trailer plus the weight of all your gear and water in the fresh tank. Use the GVWR of the trailer as the weight you will be pulling.
