I've always felt a bit of a noob when it comes to art history and art by the big historical names, so with a few hours left before I had to jump on my next train, a trip to Berlin's Gemäldegalerie in the Kulturforum to start my education was high on the priority list.
I think art collections like this are particularly valuable to a neophyte like myself because, containing a sampling of European art across a considerable time period, they give us the chance to see each piece in context (of prior art history, and of contemporaneous art movements). It's also important to get the history explaining who was paying the bills, since that was a very dominant force in determining not just what the basic material of the works was but also what aspects of it may be shown.
It's interesting to note however how the artists reacted to the constraints that imposed; for example, whereas early art was pretty dry stuff on account of it being paid for almost exclusively by the churches, who implicitly imposed a number of criteria for acceptability, there was a significant phase in which, by contrast, many artists were painting nudes for the church – because paintings of religious significance were the only ones allowed to show nudity (et cetera) and thus the only opportunity for them to make certain artistic expressions.
Anyway, the moral of the story is, definitely invest for the audio guide. It's possibly a bit verbose, so unless you have at least a full day to devote to the collection you'll find yourself skipping some of the audio guide content – but that's ok, it's still well worth it for a more moderate visit.
Ticket information here. It's a combined ticket with the other museum/galleries (and consider upgrading that further to the 3-day pass if you'll be visiting others of those on subsequent days). Incidentally, while cameras are allowed with flash off (please be careful!), you'll have to check in bags – but you don't have to pay to use the lockers, the staffed locker room next to them was free (for ticket-holding visitors, I assume).