hi Red. By a series of conicidences, I am the owner of Splendida Rainbow and Preacox rainbow fish. My tank is a 36g corner bow front. Right now I have 3 Splendida, all of them are about 4 inches and 3 baby preacox - all about 1 1/4 inches ( they will grow to 2in). The Splendidas are about full grown.
I was told I could prob have 5 of the big guys, but I am holding off right now since the tank is just recently cycled, and everyone seems to be happy.
I just looked up banded rainbow, and it gets to be the size of my splendidas. They are awesome looking.

However, now that I see their size, I wouldn't suggest a tank smaller than 30g and no more than 4 of them in that size. And I do 20 - 25% water changes weekly since I am stocked a little heavier. You really have to stay on top of the water changes if you are fully stocked, cuz things can go bad very quickly.
I also have read rainbows like to go into a maturely cycled tank - I took a huge risk, but I used Bio Spira to cycle with them. I would not suggest you put them in a very recently cycled tank, but I am just basing that on what I have read.
My groups of 3 seem fine, always moving around and together most of the time, so I think 3 is good. But I have found with most schooling fish, 3 is good, more is always better - the fish act way differently ( closer to how they would be in nature, I am thinking) and are such fun to watch. The same way the larger the tank, the better.
I have mine with corycats and bristlenose pleco which stay small. ( and a couple of apple snails).
You may have already done so, but if you Google Banded Rainbow, lots of info comes up.
Good luck with your choice, and I bet someone with more rainbow experience than I will come on and give you more info.
Val