By every kind of sport, the right warm up is very important, to bend forward some injuries of the muscles or the sinews. Because you use the whole body while surfing, you need to warm up every part of your body. It’s also important to stretch the body. 
When your muscles are warm, you can move more quickly and efficient. 
For paddling you’ll need your arms and shoulders. Warm them up with arm swings and rotate you shoulders in 360°, first smaller rotations, then bigger ones. Do ca. 8 repeats of each exercise and in each direction. 

For the right paddling position and the turns you need your neck mobility and also the muscels of your back are important. Move your neck forwards, then to the left and the right. Afterwards do neck rotations, again 8 repeats of each. For the take-off your legs has to be warmed up. Just do legs swings and akle rotations.
Afterwards stretch your body well. This little warm-up only takes about 15 minutes of your time, and with it you are more dynamic and not that prone to injuries.