I would not use a filter like the one you linked in anything under a 5 gallon tank, it will be way too strong and you would have to adjust it down and baffle it to the point water would be barely be moving through it at all and would probably burn the motor out in a pretty short amount of time, if you are bent on using a filter like that go spend 12 dollars at walmart and get a 10 gallon tank and spend another few dollars on some craft mesh and some poster hangers and divide the tank into 3 you can search the fporums here on hwo to make the dividers, it is pretty simple, a 10 gallon tank will be much easier to cycled and keep cycled plus you will only need 1 heater and 1 filter, if you want to keep your current set up of 3 little tanks, you will need 3 heaters that are really small so you do not overheat/cook the fish and I would get 3 small sponge filters and an air pump to power them all and of course tubing and a splitter to connect them all to 1 pump, but in short they are your fish and it is your choice on how you keep them, those 2 suggestions I made are good ones the 10 gallon split tank is the better of the 2 in my opinion....
I agree, only I would suggest a 20 long to divide. 10 is good, no doubt, but I think there's more flexibility with the 20 long if you have the room for it.
You'll notice on the product info it says "no adjusting necessary" - you WANT an adjustable heater. I use hydor theo heaters in my quarantine tanks - they work well. I also have an aquatop heater. My show tanks are not heated though - I'm sure someone else can provide more help in that realm.
Not a fan of Tetra heaters. I think Marineland is carried by Petsmart/co. Hydor Theos are available from most online resources (Amazon, Ken's Fish, Big al's, Marine Depot, etc.) On a 20 long, I would do one small filter at each end, or sponge filters.
I think Petsmart is still having their dollar a gallon sale.
One thing you need to keep in mind is the nitrogen cycle. There are stickies about it, that are well worth a read. Here is my short version:
Fish produce ammonia through waste. It is very toxic.
There are some "beneficial bacteria" (BB) that will begin to colonize your tank (filter, walls, decorations, substrate) that turn ammonia into nitrite. This is also toxic, but less so than ammonia. It takes awhile for your BB population to incraese enough to handle the ammonia load of your tank.
There are different BB that turn nitrIte into nitrAte. Way less toxic. You don't see these guys show up until after the BB that turn ammonia into nitrite.
Once you have established populations of these bacteria, you can do a 25-50% water change once per week.
Until you have a big colony of BB going, your fish is hanging out in toxins that can really impact health and longevity.
get a test kit. Sera and API make ones that are fine. API is way cheaper on amazon. You need tests for pH, ammonia, nitrite and nitrate. The master kit for API contains all of these.
If you have the fish in the aquarium already, you are "fish in" cycling. Not recommended because it can hurt the fish, and it is stressful for you. BUT, we have all gotten caught sometimes with a "surprise betta" that needs a tank NOW. As long as you change the water whenever ammonia gets above .25 ppm, or nitrItes above .25 ppm, or nitrAtes above 20 ppm, and keep changing until it is within acceptable parameters, you can get through it. It takes 4-6 weeks usually. Then you have a stable cycle, happy fish, and once a week (or as neccessary but I don't go under once a week) water changes.
If you choose to keep the fish in their current tanks (easier water changes) you can set the 20 up and let it cycle on its own. You will need to add pure ammonia to maintain the process. Advantage: you can let the levels get higher before changing water, and it may take less time to establish a cycle.
The stickies say it way better, but that is a brief rundown.
Petsmart has a one dollar a gallon sale now. I would go with one of those, plus an appropriately sized heater and Aquaclear or Marineland HOB filter. Only thing that could get more costly is a light if you want live plants. If not, a desk lamp or two is sufficient for the fish.
It will be less expense, and you can spend the extra on a test kit and decorations/hardscape/plants.
Tankmates are possible, since you have some room, but very much depends on the individual betta. some just are too aggressive, some don't like certain fish, etc.
Great job on setting up a wonderful environment though. Your plan works fine, I just would do it slightly differently.