Firstly, before you can start doing any of the Doomsday Heist, you will need to own a Facility in GTA 5 Online. The cheapest one will The Paleto Bay Facility, however the location is at the very far north of the map.
Nearest Facility Locations for each Doomsday Hesit (if you're doing Elite Challenges):
1) Act 1 - Grand Senora Desert
2) Act 2 - Paleto Bay
3) Act 3 - Sandy Shores
Act 1: The Data Breaches
Act 1 is probably the easiest and fastest to complete, however the Elite mode is the hardest as you really need to purchase Grand Senora Desert facility and will require you and your team to beat the 5 min timer including the entire end cutscene. If you're aiming for The Elities achivement in GTA 5 Online.
Act 2: The Bogdan Problem
Act 2 is the easiest and fastest to complete, just make sure the submarine team has enough supplies of snacks and body armor to deal with the enemies in the submarine, while the pilot / air team just have to wait near the beach without having to kill any enemies as shown in the video. Your submarine team get the job done and will have to swim back to shore, you pick them up and fly back to LSIA and land that Avenger to complete the heist.
