As the others say, the tow can be scarier than the on-track experience, and working trailer brakes are a must!
I have used an open trailer with my Spec Miata for 10 racing seasons! Started with a 95 Chevy S10, with a 4.3L engine, and was just under the tow rating for the truck. Borrowed a friend's trailer for the first event, one without brakes - what a nightmare! I was very lucky that other people stopped as I rolled through an intersection. Borrowed another with trailer brakes - and it was a huge difference. This trailer's dimensions and shape seemed to fit the Miata better too, so I bought the same model. It is a Dively Econo-trailer, open trailer - weighs ~1400 pounds - and I am not affiliated with them at all, but have had 10 good seasons with it. You can compare their dimensions to what you are looking at.
Also recommended - a weight jacking hitch. The S10 towing experience was constant work, needing huge following distances, and prepping for every intersection, but it can be done..... yet I switched to an F150 after three years.
You are smart to be concerned about not over-investing, and cash-flow, I was there too when I started. So please confirm the trailer brakes are working, and have the right connector to work with your Jeep, and good luck to you! Welcome to Spec Miata!
-DavidB