Your UTFT.zip file contains a file called UTFT_Supported_display_modules_&_controllers.pdf. This file contains a list of displays Henning Karlsen has gotten to work for himself. These should work at least on a Mega 2560 board. The UNO will only work with the smallest of boards because of memory issues and these board are often hard for fumble fingered people like me to poke at the right spot. For these reasons I always suggest that if you are working with TFT touchscreen displays, use a decent sized TFT Touchscreen (2.8" or larger), a Mega 2560 board and an appropriate shield.
In addition to some on the list that Henning Karlsen provides, I have also used 4.3", 5" and 7" SainSmart displays with a 2X20 pinset on one side. They work with UTFT but do not tell Henning that I said so. He HATES SainSmart !!!!!!. It is always good to have a brand name display of the size and type you intend to work with just in case something goes wrong while using a knockoff. It makes troubleshooting a lot easier. I have received defective/counterfeit knockoffs on e-Bay. By counterfeit, I mean the displays were never meant to work. Beware of somebody selling lingerie on e-Bay selling you any electronics.
I also tend to use the ElecFreaks TFT LCD Mega Shields V2.2. I have used knockoffs but I have also received some defective/counterfeit boards when doing so. Once again, always have a name brand board on hand so if things do not go well, you can easily troubleshoot the problem.