Just be patient. Do some research and determine what speaker brands you think might suit your taste. Lean toward vintage for the best value (JBL, EPI, Acoustic Research, Polk, just to name a few). Then search Craigslist for them every day. You will get a deal.
I don't know where you are in CA, but I found these on the SF Craigslist in two minutes. Even with the replacement woofers, I'm guessing the AR would kill any computer speakers:
http://sfbay.craigslist.org/pen/ele/1856438391.html
http://sfbay.craigslist.org/sby/ele/1858957391.html
Also, you're going to need some sort of amp or receiver, even if your TT has an internal phono preamp.
Dreamover is right: if you want to take advantage of the sound quality of vinyl, you can't do it with computer speakers.
Be patient.