So, where can I get a good comm program that has RTTY capability
(ideally freeware, to get started with) for my computer?

Go here for sound card programs. As mentioned mmtty is very good to start
with for rtty.

http://www.muenster.de/~welp/sb.htm#zvei

Here is another place to checkout. It mentions packet, but the interface is
for all sound card modes.

http://www.packetradio.com/