There are as many right & wrong ways as there are opinions in keeping this species, it is finding what works for you so that the betta thrives.
IMO/E-the Betta splendens can be kept in containers short term as small as 3 cups, key to success is "short term" and "daily" water changes.
I keep most of my betta in 1g-10g tanks unfiltered and heated, anything 3g and smaller I do 50% water changes twice a week, In my 5-10g I do 50% weekly, water changes are the key to success with any fish in any setup IMO.
Diet is also important, a good varied diet is best
2gal vase should be fine as long as you do at least 2-50% water changes a week, heaters you can find either at the LFS or on-line that are for the smaller tanks to keep a stable water temp of 78-80F
IMO/E-there are no products on the market that will cycle the tank any faster than what it will cycle, if you are on city water then you will need a dechlorinator to use with all new water added.
I don't cycle per se", in the smaller tanks, I add the fish and monitor the water making needed water changes as the water test indicate, if you don't have anyway to test the water, do 25% water changes every day for 4-6 weeks.
You want your water prams to read: ammonia 0ppm, nitrite 0ppm, nitrate 5-20ppm.
