huh you've made me see it differently. I suppose things can be two different classes. Certain patterns might skip a class or not really fit at all. very specific movement patterns cannot be replicated. Hang Cleans, snatches, powercleans do not fit as they cannot be replicated in any other manner with machine or otherwise so lets rule out the hang clean. or if not rule it out call it a two part movement one and two. Keep in mind the very nature of moving your body through space while it acts as the load increases the variabes which can be bad. Also There will be many more 2s than 1s. some muscles or movents may not even be able to be hit directly by a 1. For these the top of the hierarchy starts at 2.
Deadlift; I still say deadlift is in one. I say this because yes, you are moving a weight but its hung off of you in a fixed manner. the weight only moves as your whole bodies mass moves. Deadlift has no two or is kind of a combo of one and two. regardless that still puts it above the next closest thing which would be a combo one and three. that shrug machine that you can deadlift in . essentially just weights on a bar fixed to a pivot. This excercise is sub bar to the deadlift becasue of the addition of the level and pivot.
Push Press: I would say 2. The initial movement starts ith the whole body moving but it is only an assistant. If you look at the main function of the push press it is shoulders. You don't do it for leg growth despite driving with them. So we will assist the main mover, muscle or pattern. This being the pushing from the shoulders. During this movement Your body is stationary and the weight moves away. There is no 1 that I can think of for this exercise or a shoulder press. there are 3s' and 4s for shoulder press but no ones. The principle goes out the window due to external factors. Here being balance. TO move your body as weight in this you would have to invert and push against the ground. This might still hold value but we as humans have not adapted to pushing things while balancing on our hands upside down. There is way to much going on.
Bench Press: if you were untrained enough that a pushup had adaquate resistance it would be ideal. However most people are too strong to simply do bodyweight push ups. (which are great) the issue with the push up becomes loading. There is no way to load this that does not throuw off the movents dynamic. So once push ups must be loaded a bench press is supirior.
Squats: Squats are a 1. The majority of the bodies mass is in movement so its a 1. squats or variations are hands down the best STRENGTH builders for the legs. Squat press would be number 2. but I would throw it out again due to variables. Humans arent conditions by anything in life to adapt to that position so it is very awkward ( i would assume I do not squat press). due to this variable Skip to the next. Leg press with sliding sled for weights this is a 2/3 combo. which is still better than the leg press with pullies which I would put as a 4.
You must give some leway to the classes. this is only a rough outline. think of it in reverse. A hammer strength is better for strenght than a pully assisted machine. A barbell is better than a hammer strength. And any exercise that moves you against gravity works better than a barbell exercise so. This stays true untill funny variables come into play like balance and being upside down.
1, 2, and 3 all have great roles for bb's but for those after strength you will want to stick with the ones and twos. and 1's before 2's. I say this in reference to main lifts. assistance work may benifit greater from on 2,3 or even, 4.