Concentrate on compound movements. Do no more than 2 of them. It's difficult to convince people that they don't need incline presses, so include those if you want. A good example might be 2 sets of incline presses and a set of dips, not counting warmups. This is what it might look like:
Incline presses (I actually prefer the hammer incline machine, feels really natural)
1-3 warmup sets depending on the weight you're pushing. I'd say for every 100 lbs do a warmup set. In other words if you're doing around 200 lbs, do 2 warmup sets. Let's use 200 as an example.
100 x 5, 150 x 5, 200 x 5, 200 x 5. Only 2 worksets of 5, if done HARD, will be sufficient. When I say HARD, I don't necessarily mean total failure, but perhaps 1 rep short of it (in other words if you would fail to get a 7th rep, that would be the correct 5 rep weight). Don't sell yourself short, focus and give it your all.
Move on to dips. Use only your bodyweight until you can get 15 reps, IMO. Your upper arms should only go to parallel with the floor, any lower might stress the shoulders too much. Push to failure or 1 rep short. When you can get 15 reps with bodyweight with perfect form and without rushing through them (falling down rather than controlling yourself), start adding a 2.5 lb plate each session.
I know it's only 3 sets. But 3 sets of compound movements done hard is more than enough. I only do 2 sets, myself.
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