If you ask 10 people you're probably going to get 10 different responses, but here's my 22 cents
It sounds like your in a commercial gym with lots of equipment so I'm banking on you having access to most cables and machines?
When I'm putting a routine together for someone, I usually start them with a incline press and a fly with constant tension. I think a cable fly is best for that. You can adjust the height and the angle till you feel it more in the chest. I personally do it with dumbbells and I stay in the lower 2/3 of what most would consider full range of motion. Focus on the stretch position, Get a good stretch at the bottom on every rep.
For a 3rd exercise I like to use a seated chest press machine and if there having a chest only day I would throw in dips at the end. My shoulders don't let me do dips so I use the seated machine dip if available.
Incline smith machine press
Cable fly
Machine chest press
Dips
I also sometimes will have myself knock out 100-150 slightly wide pushups. Your doing as many sets as necessary to get there, but the goal is as few sets as possible, I try to go for broke on the first set, take a 10-15 second breather and keep grinding until Im shot or hit 150.
76, 22, 14, 10,10,10,8 was a recent one.