This will be pretty much a re-cap, but just thought I'd add on anyways.
I prefer no less than 5 gallons for my own bettas, but obviously that's a bit on the larger side (and perhaps pricier) for some people. (I currently have a divided 5 gallon, but don't call me hypocritical, since it won't stay this way for too much longer!) This is completely my own opinion .However, by DIVIDING, in the physical sense you should get a horizontal. Dividing a vertical, and doing the water changes ... will a siphon even fit in there? I'd imagine the trouble far outweighs the money-saving.
It's true, 1 gallons are possible for bettas. The main key is doing the water changes. However, I prefer meeting a betta's "physical needs" (although there is no scientific evidence to support their physical needs, I'm just way overly sympathetic. Hehehe!). This is why I prefer advising no less than 2.5 gallons. Bettas should be given room to swim gorgeously around. If for some reason the tank size is not possible, then at least meet the requirements of their health.
And let's think of the bioload dividing a 2.5gallon. 2 betta fish in a 2.5 gallon? Now, they're not big poopers. However, one betta in a 2.5 should be enough. You would be doing twice the amount of water changes (or around) to keep down the ammonia, since now there are TWO sources of poop, and not only one.
So yes, I would advice a new tank. IMO the "minimum", or rather better tank, to divide would be at minimum a 5 gallon. And a longer one at that. The 6.6 Petco Bookshelf seems to be abnormally LONG so that would fit many needs, however, it IS pricey... If you are indeed looking for dividing, the 5 gallon Walmart ($30) is the way to go.
OP, you should try looking at some pictures of divided 5 gallons. There's a COMPLETELY different feel between a divided 5, and two 2.5 gallons. I'm not saying one is better than the other - I'm saying the "feel" is different. Plus there's money, but that's always going to be a pointer. Good luck choosing, and sorry if anything brought you down!