The first thing to consider is that you will see improved results in whichever exercise you choose to open with. You are the least fatigued at the beginning of your workout, so it is intuitive that you will see the best results in whatever you choose to do first. Anecdotally, I recently put the press at the beginning of my workout (StrongLifts) and it helped break me through a huge plateau.
The second thing to consider is warming-up. I noticed when I moved to a Press->Squat structure, I didn't feel properly "warmed-up" as I went into the #2 exercise. However, this is pretty anecdotal and your mileage may vary.
The final thing to consider is the impact you will have on your subsequent exercises. Unless you are doing supersets, it is usually a good idea to have a buffer exercise separating two similar exercises. For instance, squats and deadlifts are both very similar and target a lot of the same muscle groups; it would therefore be a bad idea to do a press/squat/deadlift workout, because you wouldn't have enough recovery time between the squats and deadlifts.
As a solution to this problem, you could use press as the buffer exercise between the squat and deadlift, or alternatively you could replace the deadlift with a low-impact exercise like the bench press or rows (press/squat/bench). Either one is acceptable and depends on how flexible your workout program is.
Altogether, the final answer depends on your particular goals and what other exercises you are doing.