Depends on whether I start with more or less than 1500 influence. If more then I head straight to the bank, take out a loan and go round up the top tiers. If less then I hire the cheap guys first so I can make enough money to hire the more expensive ones as soon as possible.
If you're not focusing as much on combat then I would probably stick with mercs that have a combination of decent health plus cheap salary. Ansel, Jack, Bud, and Doyle would be great for that. Doyle is kind of expensive up front, but his salary is cheap. I don't fight with people who have less than 100 health past day 1, which excludes most of the low salary mercs.
If you're playing one of the latest versions there are a couple of unique male slaves you can capture that are absolute melee monsters but they don't go down easy. Once you get them though you have combat monsters on par with the top tiers with no salary.