Hi partshd1, welcome to the AFC - hope to see you around the site!
I have a 2003 that does not have the towing package, and I tow a pop-up camper that probably weighs in at about 1500 lbs loaded, plus likely another 600 or so for the family and cargo riding inside. I put on a tranmission cooler when I put the hitch on and I highly recommend that - from previous experience, I've seen the wear that can occur without a cooler, and my mechanic brother-in-law swears by them.
Remember that the Tek has a rating of 3500 lbs, but that's total load, not just the trailer - and generally speaking you want to not go above 85% of your capacity. Heard some stories of really bad brake wear from some other members who have towed right at the limit. I would recommend checking your brakes and making sure they're in good shape, cuz they definitely have to handle more load when you're towing, especially if you end up having to make an emergency stop after a fellow citizen cuts you off lol.
I also sprang for some cool new shocks that I can adjust via an air pump to level off the load, but those I haven't used once, the default pressure is fine, so you may not want to spend the money, as long as the ones on the Tek are in good shape.
Finally, for the hitch - a Class 1 is rated up to 2,000 lbs, but in your case I would definitely recommend going for a Class 2 hitch, which is rated for the full 3500 lbs. I have a Reese hitch and really like it.
Hope this helps a little - congrats on the new ride and be sure to update us after the trip!!