There are several kinds of reduced tickets. Most of them require an advance purchase of three days or more. If you buy a ticket at the station right before traveling it will always be a full priced ticket unless you qualify for certain discounts (being 26 or younger, being retired, etc.). Therefore it's more relaxing to buy in advance. You'd pay the same amount anyway.
If you are planning to do more travel than just to Berlin, you could also check out some of the international offers.
Regarding the seat: It's a strange concept for many, but train ticket and seat reservations are two separate purchases. A seat reservation gives you the right to take the reserved seat within a certain time after the train left the station. After that time the seat is free to take for everyone. The train ticket permits you to travel on the train to your destination on a certain route using trains classes up to the purchased level (RE, IC, ICE in that order).
I rarely sit on the seat I reserved. Usually I'm looking for a better seat that is free, such as one with a table and a power plug. But it's good to have a reserved seat as a fallback in case the train gets full which is more likely to happen in 2nd class.