A ten gallon would be a great community tank! I'm not sure about neon tetras--some bettas do ok with them, others don't seem to. Pygmy cories are great, and you can also try ADFs, basically a fish that doesn't have long fins(Like guppies!) and isn't a known fin-nipper!
The best thing you can feed bettas is pellets, followed by live/frozen blood worms and brine shrimp as snacks! Flakes are not so good, too easy to over feed, not enough nutrition!
Bettas will need a heater! Keep them at around 78-82 degrees. Filters are great, but be careful if the current is too strong!
has GREAT bettas(and other fish) if you don't mind paying shipping! A lot of the sellers are from Thailand though which will mean about 5 to 8 dollars extra on top of shipping. They ship the betta to a 'transhipper' and then the transhipper ships him to you.
Betta care seems to change from place to place..Sometimes big chains in one area will take decent care of them, other times even a small lfs will take AWFUL care of them.. look for clean water, active fish, and no diseases you can see!
Bettas like live plants but also like hides, make sure nothing is sharp! take pantyhose to test--if it rips the pantyhose, it will rip his fins!