The important factors are:

Memory type - DRAM, SRAM, etc

You will almost certainly want SRAM

Size

How much data do you need to store?
Note that memory sizes are often stated in bits - eg, a 1Mx8 bit memory has 1024K bits, organised as 128K bytes.

Speed

You will need to refer to your data sheet, and consider the clock frequency you're using

Supply voltage

depends on what's available on your board, and the requirements of your processor - another one for the datasheet.

Have you tried looking for Application Notes on the Cypress web site?

Are there any reference designs? Can you find the schematics of any eval boards? - looking at these should give some hints.