I just wanted to share what I ended up doing!
I ordered the 5 gallon Hawkeye tank from Wal-Mart for 27 dollars and the 25 watt Hydor Theo heater ($16.79 on Amazon.com with free 2-day shipping; got here in one day!). I heard great things about both of these, and so far I'm loving what's happening.
The fish tank came in today, so I just rinsed all the accessories I got for it and got it set up. I'm monitoring the temperature with the heater, and the heater thermostat seems to be spot on maintaining 79 degrees. I slowed down the filter (picture was taken before that, so you can see the bubbles flying around from the too-strong flow) by rubber banding filter sponge into the outtake. I'm going to let the tank run for about 24 hours before floating him. Going to do the whole deal with water exchange, even though he's in the exact same water at the moment just to be extra safe (I do that every time I clean his tank).
The plant in his current tiny tank is expandable and can be twice the size it is in the picture, so that'll be in there as well (I am NOT putting any of the gravel in the tank besides what's going to hold the plants down- I hate it, it's sharp and he likes to sleep perched on the bottom, and it's scratching up the current tank and I don't want that happening to this one) and I'll get a real plant next week when I get back from home. I tested all the stuff in there to make sure it's not too pointy. :)
He seems really excited to get in there and I can't wait to watch him swim around in it. I feel kind of mean putting him right up next to the tank (he tries to swim into it :( ), but there's nowhere else to put him without putting him in the A/C draft so he'll just have to yearn to be in there for a day. :P
I have everything hooked up to a GFCI outlet, as this room has one since there's a sink. I have a gravel vacuum. Believe it or not, we have a lot of fish/fish tanks at home (55 gallon, 25 gallon, 10 gallon, 10 gallon cichlid, 10 gallon salt water, all cycled). They're all my mom's and my sister's, but I didn't come away with absolutely no knowledge. Never had bettas, though.
I think I answered all the potential questions!