I'm working on exactly this style of project now using cheap 433Mhz xmit/rrecv pairs. I have got the transmitter working fine (using TX pin) with the connection to the computer at the same time but the receiver is still having problems starting up on the RX pin for a reason yet undetermined.
That said, I can get it working with a manual tweak and using h/w send and receive works fine.
Try these ones on Sparkfun (or ones like them) and see how you go.
That page also has code and a walkthrough for doing it all on Arduino...it just doesn't seem to work with either my versions of the xmit/recv or maybe its the newer Arduinos.
Ben