Selecting external RAM for an ARM static memory controller
The peripherals listed there typically have "asynchronous" busses -- that is, the simple and familiar type with address lines, data lines, and a couple of control and latch lines.  This means that the SMC is not meant to work with SDRAM, DDRAM, or other subspecies of synchronous dynamic RAM: it's meant to work with regular ol' asynchronous static RAM, so that's what you'll probably want to look for.

You can also use PSRAM (Pseudo-Static RAM) with the SMC.  PSRAMs are dynamic RAM chips with a controller tacked on that imitates an asynchronous RAM, and takes care of all the messy refresh chores for you.  Since they're dynamic RAM inside, they can be very large and relatively cheap.  The downside is that they're also slow, like dynamic RAM.

You probably don't want dual-port or quad-port RAM.  If you needed it, you would almost certainly be looking for it specifically.