@longpole

You didn't mention if you plan to use monochrome or colour graphics. Monochrome is easier to handle. Wonder if you looked at the storage requirements. A 320x240 single color bitmap needs 9600 bytes of storage. Assuming this needs to be in 16 bit color, the storage need gets up to 153600 bytes. 320x240x16/8.

A high cpu speed is definitely a must and you will need to hand-optimize the output to be able to refresh the LCD fast. Otherwise the display refresh will appear very sluggish.

A PIC with a PMP peripheral will make a good choice for such an application.(I did not check the datasheets for mentioned Ics)

If you wish to make a frame buffer, lots of RAM will be needed.