Most microcontrollers (microconttrollers are microprocessors with built in memory and peripherals) have a UART that will communicate with a standard serial device if you use a simple level shilter(to get the right voltages) like the MAX232. Your best bet is to buy a cheap development kit with a microcontroller and MAX232 already on board. Then you just buy a RS232 crossover cable (it just switches the receive and transmit lines)to talk to your device. Zilog's Z8encore dev kit is $39 and I've heard its quite good. Atmel's AVR kit is fairly good too. I'm sure there are a million PIC boards out there.
Brent