Got it!
First things first, I successfully entered programming mode on the Solara tonight by following these steps:
http://www.programyourremote.com/classified/DisplayAd.asp?id=1218
and it worked, because after I did all this stuff the locks cycled twice, telling me a) that it has RKE, and b) that I was in programming mode. I didn't have a remote to test it with, but I'm ordering one tonight and when it comes in I'll report back. I was tempted to see if I could program the spare key from my Tacoma to open it, but in all likelihood it won't work.
Second, thanks speedkar9! It's the SE model, V6, 5 speed. Everything works. It's got 232K and change, so it's just getting broken in. I drove it over 125 miles tonight just bringing it home, and I'm in LOVE. Rides great, runs great, unless it blows up real quick it was a steal at $1500. First step is new timing belt since I have no maintenance records, next is bodywork cause from the looks of the sides of the car, this dude scraped the side of the car next to him EVERY TIME he went to the store.
I'll get some decent pictures up soon cause you know, we all love to show off our toys.