Most betta starter fish are just torture chambers. I work at petco and I admit that pretty much all of the "starter kits" for goldfish and/or bettas are terrible.
Bettas are tropical fish, very hardy fish but they still should be treated as any other fish. They need warm water and yup they do need a filter since tons of beneficial bacteria will be stored there. (Read up about the nitrogen cycle here: http://www.fishlore.com/NitrogenCycle.htm)
For a single betta, I recommend a 5gal tank, or a 2.5 at the bare minimum... but it's harder to keep good water conditions in a tank that small. If you bump it up to 10 gals (which is actually cheaper than the smaller ones since it's so common -- you'll find it at pet stores at $11) you can mix different fish in there. IMO, no tank is complete without bottom feeders like corycats and a small school of fish makes it awesome!
