My LCD has four connection communication methods, Ethernet port, wifi, Bluetooth, and UART.
Here is the specific data sheet for my screen.
Which method is the easiest for FPGA to drive through?
UART by far. Ethernet, Wifi and Bluetooth with require IP cores that while available, are not free. If you try and create your own cores you'll discover they are very big and likely will take a lot of time.
UART is a simple protocol that should be possible to implement fairly quickly.