1-3 will all work, but at a cost (delay) to the development of the hive. #3 delays population growth for 30 days. Your goal as a beekeeper is to have an optimum population count just before honey flows in your area.
Using #3 you will likely miss robust growth with the first honey flow. 1 & 2 wastes ten less days than #1, that is good. An introduced queen can start laying right after she is released. Read up on a
'push-in' cage for introducing queens, it is the best method when it works.
One way to get a queen with less handicap to the hive is to break out a small NUC. If you have swarm cells for that NUC, all the better. Swarms cells will likely produce well nourished queens, better than those from a walk away split. Well nourished queens, from larva chosen by the bees will be better queens in the long run. JMO
P.S. You will do well to prepare a bait hive to lure a swarm into your bee hive. Those bees come with a queen, are free and preprogrammed to go like crazy.