The CFAF320480C5-035T-TS can work with any number of micro-controllers. There are a lot actually.
Besides driving the display, what else will your device be doing? The more that you'll be doing, the "more" of a micro-controller that you will need. One advantage of the CFAF320480C5-035T-TS is that it does support a number of different interfaces; 16-bit Parallel, 18-bit Parallel, 8-bit Parallel, 9-bit Parallel, DOT-CLK interface / Generic RGB, or SPI. The 8, 9, 16, and 18 bit parallel interfaces are also called "MPU interfaces".
Some micro-controllers have built in support for displays, in particular TFT displays. There are typically limitations to that support - - such as which interface is supported, or specific controllers. Our display has the Himax HX8357-B, or compatible display controller.
We have worked with Cypress, STMicro, and Atmel micro-controllers. These are only a few of the many available. From Cypress, look at the PSoC4 line, or possibly the PSoC 5. From STMicro it's more about how much processor you want. Our CFA735 / CFA835 is built around the STM32 series. From Atmel, the ATMega line should be adequate with the AVR32 being quite capable.
