Like Spiffy, usually I'm a casual rider-- so I use the first few blocks or so as a warm up, then if I feel I need to stretch I stand on the pedals and drop my heels to stretch my calves. That's usually it.
But then again, sometimes I get in "serious rider" mode, so I'll stretch hamstrings, quads, calves, etc after warming up a bit, and again when I get done riding. I qualify "serious riding" as a recreational ride, not a commute ride.
For hands: switch hand positions occasionally. If you're not used to riding with drop bars, you probably aren't used to the hand position for using the brakes yet. Or, if you're like me, you have tendinitis in your hands, so you have to do extra stretches (wide open hand, then fist, usually, then shake it out) for your hand just to keep pain at a minimum anyway.
Welcome to the forums!