Welcome to the forum! (We love pictures!)
Personally, your betta (who sounds lovely by the way!) would be a lot happier in a larger tank. If I were you, I would put him in the 10 gallon. It's definitely not too big, and you can get more ghost shrimp. They're known to have short lives, and some bettas love to pick on them.
Or, if you prefer, you can get snails. They poop a LOT, but they're way too cute!
In a 1 gallon, you would have to do water changes every single day since ammonia builds up fast in such a small amount of water. In a 10g, you would have to do water changes a lot less.
Octavius - Male Halfmoon [02/19/11]RIP
Nero- who had been living under the moniker of "Hestia" for the past two months. Poor boy. [02/28/11]