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Strength Training Workout Idea - Suggestions?

So I like strength training... sort of. Early next year I'm going to hire a trainer to help me be more strategic with it.

I'm thinking of doing something like this:

Ladders 1-10-1 Reps
Barbell Squats
Push Ups
Overhead Press
3xWeek (MWF likely)

So like this:
1 Squat
1 Push Up
1 Overhead Press

2 Squats
2 Push Ups
2 Overhead Presses

(And so on up to 10 reps and back down to 1 rep.)

I read that doing something like this you don't rest between sets, (unless safety requires that.)

Thoughts? Would this be good to do for say 6 weeks?

I adapted the idea from this article. And Stronglifts.