Warming up before an exercise routine, workout, or going for a run is always a good idea. Most research shows that dynamic stretching is more beneficial to get blood flowing & muscles loose or warmed up.
Standing in place, quicker shorter movements will help get everything warmed up. Hip flexion/extension and abduction/adduction are great to dynamic stretches to start with.
Then going into some movement, soldier march with a twist and hamstring curls with arm raises will get the lower body as well as the back and arms warmed up.
Side squats and marches with a push off are also great to get the whole body moving.
Finally, a squat with touching the floor and reaching up will help get the body warmed up and ready for a workout.