I'm not a huge fan of the automatic vitals-taker contraptions, though if you are in a rush for time during a serious emergency, they can be helpful.
If the pulse is strong and regular, 15 seconds will do. If there is something off, go for 30 or 60. Oh, and if you are taking the apical pulse, always do it for 60.
Respirations depend on your experience, really. If you are inexperienced with taking them, count the pulse for 15, and then count the chest rise/fall for 15 more with your hand still in place. The pt will think you are still counting the pulse, and their respirations will change if they know you are counting the respirations.
If you are experienced, you probably don't have to use any little tricks like that. I have a partner who can tell how fast someone is breathing from ten feet away. :wacko: