Hello, if you will use an lcd and touchscreen combo,
I've had luck with 2.8" lcd with 37pins, for example ebay #200659767038, I didnt
buy from this seller and dont know how are their lcd's, but that kind if interface is easy
to find around from multiple sources. Touchscreen interface using the uC itself
it's not hard, but there are also dedicated ic's.
The higher end CM3 can drive the interface directly as a memory mapped
device, for example FSMC of some STM32.
Ciao,
Fabio.