I often sing the praises of the Innova Standard bag or its similarly-sized contemporaries (Crunch Box? Squirrel Monkey?). For someone--like myself--still learning all the intricate details of throwing mechanics and different discs, it's really all you need. 8-10 discs, a nice-size drink holder, a towel ring, and pockets for all your loose crap (phone, keys, marker, scorecard, snackums).
I will say that of the courses I play, none are more than 18 holes and each has at least one place to refill water. For competitions where I'd want more options or on a longer, more grueling course, I might consider a larger bag.