Which avoidance maneuver is best when seeing crossing traffic on approach to a runway? Let us say I am in final landing and I saw another aircraft is crossing the runway while I am still in air, should go around be my best choice? 

If I touched down and then I saw the traffic, how could I make the best decision to avoid the conflicting traffic, increase throttle to go around, or increase brake force to stop before the impact, or decease the speed and try to exit the runway at a high speed?
When you are on short final and something is on, is entering, or even seems to be entering the runway, you execute a go around. 

As for the second part of your question, given the loose parameters I'm afraid there is an infinite amount of different scenarios, and therefor I can't provide a comprehensive answer.