Good job on getting him a proper sized tank. Many filters are too strong for a long-finned betta to be comfortable with, but there are ways to soften the flow of from the outlet using things you might have around the house. Look in the Betta Habitats section of the forum and you should see a sticky on DIY filter baffles.
Keep in mind that it is not as simple as putting water in the tank and adding a filter. It isn't the filter itself that keeps the water clean and livable for your fish--people use filters because the media inside the filter becomes a habitat for beneficial bacteria which feed on the ammonia your fish releases as waste, turning it into nitrite, and then nitrate. Ammonia and nitrite are very toxic, any detectable level of either chemical can be harmful to your fish, this is why uncycled/unfiltered containers need 100% water changes. However, once your filter has been colonized by bacteria, you only have to worry about keeping nitrates under control, and nitrate is much less toxic, so you only need to do once weekly partial changes once the nitrogen cycle is completed.
Please take the time to research the Nitrogen cycle and how to perform a cycle safely. If you want to cycle your tank with your fish in it, you must purchase a good liquid test kit, such as this one: http://www.fosterandsmithaquatics.co...fm?pcatid=4454
Because the population of bacteria will be fluctuating during the cycle, the only way to determine when a water change is necessary and how far along you are in the cycling process is to test the water. Make sure you get a liquid test kit--strips are very expensive per test and quite inaccurate.