Welcome to the forum and to the wonderful world of Betta keeping.....
The best water test product is one you will use and can understand-although a lot of negative things are said about the test strips...IMO/E they are fine and will give accurate enough reading for most hobbyist, however, if you are changing the pH (not needed or recommended) the liquid reagent is a better choice or if you are fishless cycling.
The liquid reagent type test are good, however, they have a big margin for user error-due to the multi step required to use them.
Then you have the results of these test and understanding what they mean, what to do about them and what can cause changes and/or skewed results.
I highly recommend any level hobbyist to have some type of testing product-be it the test strips or liquid reagent and research about water quality and what the test mean in regards to cause and effect, with that said....IMO- you don't have to have water test products on hand to successfully keep Bettas...you can always take water to the pet shop for free test if needed......
A 2.5gal tank can cycle, however, due to limited surface area for the nitrifying bacteria the nitrogen cycle is not always stable and twice weekly water changes are still recommended to maintain water quality regardless of cycling stage.
Unless you have a filter-the 2.5gal tank will not cycle properly-the nitrifying bacteria need-surface area, oxygen and a food source to colonize.
Water prams you want to test-ammonia, nitrite, nitrate and pH...remembering that pH, KH/GH, live plants, some dechlorinators and other additives can change and/or skew test results.
You also have other things that we don't test for that can be harmful like-heavy metals and DOC's (dissolved organic compounds)