Yes 4-6 inches. If your aging the water it's all the necessary things as in a heater as well, I'd suggest 6-8 inches because when water is heated, it evaporates. It all depends on how long you plan on aging it before use.
4 inches is best. It helps the male keep the eggs and fry in the nest as they don't have as far to fall.
Read up on breeding Betta's so you don't make the mistakes so often seen here.
The number one priority: Clean Water!!!! Sounds simple and it is, until you neglect it and then it all falls apart. First poisoning from the build up of toxins, then disease follows with the loss of immunity and they become easy pray for parasites as well.. Ick, Velvet.... Make your life easy, keep the water clean.
The amount of water doesn't really matter. I've used 4" up to 12 - 16" water. It's personal preference. But perhaps you should try the shallow method first 4-6" of water to later add 1g daily once fry are free swimming..
I have a sponge filer I bought, but, was unsure when I should add it in.
I go ahead and install the filter before spawning, and turn it off when adding the fish until the fry are free swimming for 2 or three days. Just start it up slowly and pick it up as they learn to swim better. You will also be adding water for the first couple weeks until the tank is full so that will help keep the water fresh. I try to limit my vacuuming when the fry are so tiny that I cannot see them, that is why I also am careful to not over feed.
Since I spawn using a more natural method-I use 10-12 inch of water or full to the top in a dirt based heavy planted tank.
Outside I spawn in 5gal bucket that are roughly 18 inches deep.
In an experiment I conducted-I gave the male a choice between deep and shallow water and he picked the deep end.......
IMO/E-Water level doesn't have any impact on egg/fry development-The lower water level has been used and recommended more due to the long heavy fin males having problems carrying their fins and swimming to and fro collecting eggs/fry, however, if the male is healthy, properly conditioned..etc......it shouldn't be an issue.
Often with lower water level and long fins they can be the cause of more accidental disturbance of the nest that cause the eggs/fry to fall-causing them to work even harder/longer.
In my spawning tanks-I rarely see eggs/fry fall from the nest even if you tap on the top of the nest anchor.....they don't fall-I can even scoop the nest out to artificial hatch and rarely will see eggs on the floor of the hatch container....
With all that said......IMO-when its your first spawn attempt....using the standard hobbyist method is the best method to use-
Bare bottom, half full 10gal without a filter, common snails, tannins, top covered with plastic veggie wrap to retain heat/humidity, water temp 80F and if possible...lots and lots of live plants to functions as a natural divider to prevent premature egg drops, promote microorganism development and cover for both the breeders and fry.
As for your spawning tank now-what I would recommend-fill it up, turn the sponge filter on, add a couple of common snails and lots of live plants-
Then feed the snails fresh blanched or raw greens-like spinach, lettuce...etc.....this will help get a good colony of microorganism/Infusoria growing for the fry to free range feed for several days. This will give them a good head start before you start feeding them other live foods.
This needs to be done at least 2 weeks before you plan to spawn.
Make a 50% water change in week one and add a tannin source-
Then again 2 days before you plan to spawn-using pre-tanned replacement water -
Then the day you plan to add the breeders-lower the water level by 2-3 inches by siphoning the mulm/debris off the bottom-and turn off the sponge filter.....
Have some pre-tanned water on hand to start adding by gravity to the tank after their first feeding-about half to 1gal daily until full and turn the sponge filter on as low as possible.
Once full-start making 50% daily and vacuuming the mulm/debris off the bottom....Start increasing the sponge filter output.
Be sure and check the waste bucket for fry that get siphoned out.