It sounds like it would be cheaper to get the 10 gallon.. even though 5 gallons are cheaper everything you have to get x2 will be MUCH more expensive.
You can very cheaply make a divider out of plastic mesh and plastic report binder edges.
You really need to cycle a 10 gal and you can either do it fish in or fishless.. since you are pretty much new to betta care I would HIGHLY recommend a fishless cycle. Make sure you research how to cycle properly.
For whatever tank you get you'll need:
hood (preferably with a fluorescent light)
filter (make sure it is strong enough to fit your tank)
heater (25w for a 5gal and 50w for a 10gal.. Also make sure you get a heater that is adjustable)
plants (live or silk is best but plastic is ok as long as it passes the pantyhose test)
thermometer (glass in-tank are best)
Water conditioner (highly recommend prime)
bucket marked FISH ONLY (for doing water changes)
For your fish you need;
a good pellet
frozen or freeze dried blood worms or brine shrimp (I don't recommend freeze dried be fed more that 2 times a week)
aquarium salt (to add to the tank if your fish gets sick)
Make sure you keep the cups they come it as they can be useful if you need to take the fish out for aquarium maintenance.