In my opinion, you should usually do first the exercise which (a) requires more coordination and (b) activates the greater amount of muscle mass.
As squats fulfil both of those criteria, If I were you, I would do squats first.
Just from a safety point of view, I've never liked the idea of squatting with pre-exhausted thighs - I think it's a recipe for disaster. Leg press is a much more controllable exercise that doesn't require any element of balance.
Powerlifts: 500/363/573 @ 220 belt only
front squat: 403
dips: bodyweight + 176 x 4
military press: 232