Big thanks to everyone on this forums for their help, especially
for his patience in the newbie cycling thread.
I finally have my first tank set up (and feel like I understand it reasonably well) so I went out and purchased a betta last weekend. There wasn't a lot of inventory at the store so I just chose the sickest looking one in the dirtiest looking cup and figured this might give him a second chance at life. I've had him three days now and he seems much improved. He's in a seven gallon tank with a legitimate 5 gallons of swimming space, a nice heater to keep things warm, and the pH is perfect for him.
Thanks again everyone for your help!