If there isn't a local tribe of savages on your deserted island, I'll change item 1) with: local tribe of savages :D
Bullshit! You let Thrill Kill bring like 10 different items in her "survival knife kit".
Plus, a tiger obedient to me would never attack my companions out of the blue ffs.
Ok, then : tiger, beautiful doctor and I'm confident the savages would want me as their leader only because of my strength/fighting skills and fascinating knowledge. I'd like the fireworks though to pique their interest and stop their initial savage attack on me.
Food and shelter, at first, I guess. I didn't really think this through, but with a tribe of savages under my command things would be much easier from a survival pov. I'd try to make them happy by teaching them to be better fighters and make more efficient weapons so they wouldn't turn against me and cook me, the doctor and the tiger for some reason haha.