Lots of folks Flat Tow (dingy tow, 4-wheel down tow and Toad are all acceptable terms for this) a Jeep because they are easy to put into a neutral tow with the 4-wheel drive system. But not every Jeep model. Make sure the get the correct version of the system.
The Mini Cooper is not as popular. First, it must be a manual transmission - you can't tow a Mini with an automatic transmission. And second, the Mini Owner's Manual expressly forbids flat towing... even in cars with a manual. But that doesn't mean that you can't do it. Many folks do tow the manual Mimi successfully. I looked at buying one once and the selling dealer even told me that if I flat towed it that it would void the warranty.
Most Chevy SUVs and many Ford and Lincoln SUVs and cars are flat towable even with an automatic.
The most popular Toad was the Honda CRV but in 2015 Honda changed the automatic transmission to a CVT and so anything newer than a 2014 can no longer be flat towed.
You need to look at the Good Sam Flat Towing guide or the FMCA Towing Guide. They put out a new version every year. So, if using a used car you need to find a PDF copy of the towing guide for the same year as the car.
Here's a link to the Good Sam Guides: