Fellow newbie here, we bought our first travel trailer two weeks ago and I had big concerns about sway as I was pushing our 2002 Suburban to it's weight limits. I posted on this website and considered all the advice given on my post titled "anyone with experience towing with a suburban". The advice was valuable and I towed it about 836 miles from Idaho to our home in California.
We had no sway issues. A slight pull to the left of the entire rig as trucks passed but that was all.
I also gained a lot of confidence by weighing my rig and checking tongue weight. The local refuse site allowed me to use their scales for free giving me my Gross Vehicle Weight. I then weighed it per axle on CAT scales to calculate all my weights. My weights were a surprise and I definitely would weigh your rig.
After that we used a Husky weight distributing hitch, one friction type anti-sway bar, a Tekonsha P3 brake controller and LT tires on the suburban.
For me backing up is hard (either parallel parking or 90 degrees into a space is hard). It is a 30 foot trailer. It takes 15 minutes each time. Backing up at night is even worse. I've been doing it without someone directing me.
We never had instructions for our hitch and didn't put grease where we were supposed to. It now shows considerable signs of wear. We had a dealer set it up for us to make sure it was right but he must have assumed I would have know that. I expect to have to buy a new hitch at some point.
So we're now looking forward to our first proper trip. This weekend was cancelled due to snow in the Sierras.