I'd have to second the post by Chris KI6WUR regarding EchoLink. It's a fast way to get on the air once you appear in the ULS. No radio is needed, just the software and a Technician license, this way you get on the air while saving for that first radio.
Regarding connecting Radios and Computers there are many different was to do this as well as several modes of data you can use to transmit (Rtty, PSK31) just to name a few. Check out the Amateur forums on this site as well as EHam, and ARRL for more useful information on this subject.