You do not need a filter with a betta, you are correct.
In place of a filter, you would be wanting to do 100% water changes.. it all depends on the size of the tank, and whether or not you will have any live plants.
For no filter anything under 5 gallons you are wanting to do 1 50% and 1 100% per week.
For no filter, 5 gallons and up you are looking at 1 50% per week (with vacuuming) and 1 100% per month.
You can technically cycle a smaller tank that is under 5 gallons, but because the surface area is so small, the cycle won't be stable and can easily crash time and again. As mentioned above, it's after years of building and making a perfect eco system within their aquariums that they can get a small tank to hold a cycle relatively stable.
If you do opt for a filter you can baffle it by cutting and placing an aquarium sponge in the outflow section and held in by a clean/new rubber band. That will help keep the flow low.
For filtered tanks below 5 gallons you are wanting to do a 50% water only and a 50% siphoning each week.
For filtered tanks 5 gallons and up you are looking at roughly 1 50% with siphoning per week.
Again, this is based on no live plants.
Live plants will cut down the % of water changes per week.
They do rarely use their gills, and they prefer no current if possible- which you are correct. Some current won't harm them if it's minimal, just as long as it doesn't cause them to work hard at swimming.
Good luck, and go by your gut and your research before the words of some of the store employees.. sadly, they have caused so many deaths to these fish by giving wrong advice. At least this one didn't fight you on wanting a larger tank for a betta ;)