I tow a 2017 KZ Sportsmen Classic 180bh with my 2006 Kia Sedona EX minivan. Even after upgrading to a larger fridge and a.c. unit, the weight of the travel trailer was only 2700 lbs. The 180bh has bunkbeds and a queen size bed with a regular mattress. It also has a large closet to hang your clothes. Some of the models you have looked at have no closet space at all. Also, 3,000lbs unloaded is too much for your minivan. Add the weight of the passengers and you will be over your weight limit.
Also, I highly recommend that you make a few changes to your minivan. Have the largest external transmission cooler added. I put Timbren suspension springs on the rear, E2 weight distribution hitch with built in sway control, and a brake controller.
The most important thing I did was to get the dealer to let me do a test tow before purchasing the travel trailer. The dealer let me test tow a used trailer that weighed several hundred pounds more than the one I was purchasing. This extra weight will account for a fully loaded travel trailer.
If the dealer will not do this, either rent a trailer for a day or find someone who has one for sale that will allow you to do so.
I have no problem towing with my Kia but you have a different minivan. I suggest you have the hitch installed first and then do a test tow before you invest money in the upgrades to your minivan. This way you will know if your vehicle can handle towing the travel trailer.
Another thing I do is travel with my water tanks empty and purchase most of my groceries after arriving at my destination.
