You can have your lower body on day 1 and 3 if you like. Personal preference there. Having both upper body lifts back to back might leads to some recovery issues, particularly if BP is before PR.
On a four day split where the four main lifts are done once per week (Mon-Bench Press, Tue-Squat, Th-Press, Fri-DL), what's the difference between doing Bench Press on day one vs. Squat on day one? My initial assumption is that doing Squats on the first day may have a negative affect on the BP the second day - and the BP wouldn't affect the Squats the same way Squats could affect the BP. However, I've seen it done both ways (I think). I understand that the upper body and lower body lifts need to be alternated, and why. What's the reasoning for Squatting or Benching on day one? (And if this is addressed in Practical Programming just say so and I'll look again.) Is this simply personal preference?
You can have your lower body on day 1 and 3 if you like. Personal preference there. Having both upper body lifts back to back might leads to some recovery issues, particularly if BP is before PR.
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I think you have a good grasp on it. Heavy squats and deadlifts can hurt your pressing workouts, but pressing really doesn't have a big impact your squat and deadlift sessions. So do pressing first with squat or deads the next day. Take a day or two off to recover from the lower body session, then do it again.
I believe this is mentioned in PPST3 somewhere as a sidebar comment, I'd I come across it I'll let you know. But like I said, I think you have a hold on it.
Certainly doesn't mean you can't do it the other way and make progress. I would say it depends on how consistent you are day-to-day and week-to-week. If you have a tough schedule and miss more workouts then you'd like, I'd squat first to make sure you get it in that week.
This can be found on page 149 of PPST3 in regards to the competitive powerlifters training split. Perhaps not as relevant to the one lift per day split since in this you're not squatting and deadlifting the same day.
"The bench press is best trained the day before the squat so that it is not affected by the fatigue produced by squatting and deadlifting."