What's the best 'favor' to select? What benefits do I get for being a King? I think I can get into the Strip with 2000 caps, I just need to work for it, shouldn't be to hard.

Also, can Rex the dog die on my way to Jacobstown? King just lays him on me when I didn't want to do the quest at the time.

If you want to make your life easier, save the favor for a later quest.

He can only die if you're in hardcoe mode. If you don't want to deal with the quest right now you can just dismiss him like any companion and he'll go back to Freeside. Then you can pick him up again whenever you want or not at all.

If you're doing the NCR ending, don't take the favor. It comes in handy later.

If you're not doing the NCR ending, take the caps and buy some bubblegum with it.