Here is a list of what can go with bettas. Some people might not agree based on experiences, but it all depends on the individual fish. If you notice shredded fins or agression, try to find the culprit and trade him in:
Mollies
Cherry Barb
Clown Loach
Zebra Danio
White Cloud Minnow
Cory Cats (Corydoras)
Cardinal/Neon Tetra
Platies
Ghost Shrimp
African Dwarf Frog (Don't mistake it for the CLAWED frog)
Corys . . . not paleatus . .. they are too small. Haven't had any bad experience with corys. Mixed results with other fish.
Gems is right, bettas are very individual.
I think that filter is going to be too small for a 10 gallon. I have a couple of them in 2.5 gallon tanks. It's rated for anything between a 2.5-5 gallon. You are going to have to get the next larger size IMO.
yeah, i agree, it's too small of a filter to do a decent job. get a cheap filter that hangs off the back, i think they're no more then 20 dollars or so. it'll be worth it, trust me.