You may want to look into Papillons. The breed excels in both obedience and agility. An added bonus is that they aren't destructive or nippy like the herding breeds.

Rottweilers will do well in both, but they are quite a bit to handle on an agility course. They simply aren't very agile once they fill out and their prey drive tends to send them to the gallery looking for friends/victims. It takes a firm, strong hand to gain the upper hand with them and, until they are trained to obey, it may not be a good idea to do agility. They do have a mind and like to use it to challenge you.

Beagles, unfortunately, are not very trainable. This is not to say that they cannot be trained, but it takes far more patience and time. You will probably have an agility/obedience beagle with about five years of regular and intense training.

GSDs are great for obedience, but they are built for strength, not speed. They do not regularly perform well in agility as a result. You have to remember that agility is a timed sport so speed is a big factor.

Some of the greatest agility dogs are small. A few that come to mind are Jack Russel terriers, Fox terriers, and Papillons. Of these, the Papillon is the easiest to train and the most intelligent.
Of course, if you don't want a small dog, you will pretty much have to go with a herding breed...