Hi! I must ask, is his bowl at least heated?
Otherwise, I'm very happy he's much healthier than when you first got him! Looks like he's enjoying a nice life. But a bigger tank is always better! It's easier to maintain and in some ways, to clean. If you had a 10 gallon tank you could split it in half so they each had 5 gallons, or you could split it into 3 to give each about 3.8 gallons which is the most I would split a 10 gallon.
If you wanted four fish I would consider a 20 gallon long, but you said you were pressed for space? Anyway, live plants in the tank is almost always a good thing! You can get low light plants like Anubias, Hornwort and java ferns which will all do very well. You'll have to pick off dead leaves every now and then but it's not so bad.
Plants don't necessarily keep the tank clean, but it does help filter water a little. The main thing is that they use Nitrates for food. I assume you don't know much about a cycle yet? When persueing a larger tank, it would be best to do a Fishless Cycle to get it ready for your Bettas. I suggest you google it and look at some pictures :) It might take a little while to understand but it's very beneficial to your fish and helps so you don't have to change their water every other day to keep the ammonia down.
So you can get kits for 10 gallons that come with a filter and a hood and stuff. But honestly I never like the hoods or the filters that come with kits so it might be beneficial for you if you just bought one of the 13-14 dollar 10 gallon tanks at Wal-Mart, they also have a LED light hood that is only about 20 bucks. And then you'll just need a good heater (I suggest one with a dial on the top so you can change the temperature when you want since most heaters will stay around 78 degrees, but for some of my Bettas they really like 80 degrees and hate anything under it lol, picky fish) and then you can get a Hang on the back filter (HOB filter) so that you can baffle the outflow of the water with this: http://www.bettafish.com/showthread.php?t=30139
I actually just cut the bottle section in half and only use half to go over the flow instead of the whole thing like you see in the link and then just duct tape it to the lid.
Buuut anywho, I think that's all I can think of for now lol If you've got any questions feel free to ask them ^^