Heres a nice little place that describes how to do a fishless cycle rather well IMO ;)
Lets see....a slandered 5 gallon glass tank is about 18" long, 8" wide, and 10" tall :)
I wouldn't suggest a tank-mate for him in a 5 gallon....there are very, very few options, and he'd probably be happier living on his own in such a small tank anyway ;)
Though...a 5 gallon does give room for diving, if you end up finding a second little friend you just can't resist...xD
For your first fish, I would suggest a local store or Petco. Walmart and Petsmart generally keep their fish in rather poor conditions and you don't want to get a sick betta for your first one. Petco has a wide variety of tail types, and they don't keep their betta's in quite as bad condition as Petsmart or Walmart, in my experience. Local places can always be fun to check out as well...you never know what you'll find there ;)
Though if you see a betta that just calls out to you...get him, regardless of where hes from. xD