its good that you want to ride to get in shape.

while it CAN be done on a single speed, a multispeed bike can let you be more comfortable over long distances. multiple gears will open up more possibilities for training, like longer steeper hills, faster and more variable paces, intervals etc.

if you just want to get some good cardio exercise in addition to getting around town, a single speed will be fine by itself, but a geared bike is the better trainer if you are looking to become a more serious cyclist.

EDIT im not trying to discourage you by any means, just saying that if the bug really bites you, you will eventually want a geared road bike.