Enough about the "Big 3" already. As a non-powerlifter and someone who trains non-powerlifters, I get annoyed with the powerlifting mentality that often seeps into the rest of the strength training world that places the bench press, squat, and deadlift on top of the exercise hierarchy as primary lifts and relegates everything else as secondary, accessory, or assistance exercises.
That sentiment makes sense if you're competing in powerlifting since your goal is to improve those three lifts, but if you're not a powerlifter and just lift to look better and get stronger, it's silly. There's nothing wrong with the Big 3, but for the non-powerlifter, there's nothing magical about them either. For general strength-building and physique purposes they may be the right choice for you, but then again, they might not be. As with most things in fitness and in life, it depends.
I do like the idea of having several primary lifts as staples in your program to provide continuity, because it's hard to gauge progress or get stronger if you're constantly switching exercises all the time. They just don't have to be the bench, squat, and deadlift. Any compound exercise can be a primary lift, provided you treat it as such, meaning you make it a priority in your program.
What you choose as your primary lifts should depend on your goals, your anthropometry, and your injury history.
Assuming your goals are aesthetic in nature, ask yourself the following question to help determine what should be your primary lifts.
Based on my anthropometry and injury history, if I could only do three exercises, what would I pick to build my best overall body?
This might be a press variation, a squat variation, and a deadlift variation, similar to the idea of the powerlifting Big 3 – only not necessarily the flat bench press, the back squat, and the conventional deadlift. Or it might an upper body press, an upper body pull, and a lower body exercise. However you decide to pick your exercises, be sure to select compound movements with high loading potential that can be progressed over time.
The bench press is undoubtedly a fantastic exercise for both strength and muscle building and could certainly be a good candidate to be your primary pressing exercise. That's assuming you can do it pain-free and you actually feel it in your chest.
Many people find that the bench press bothers their shoulders though, especially those with preexisting shoulder issues. If that's you, you might be better served focusing on floor presses, board presses, dumbbell press variations, or even the dumbbell floor press. Many people find using a low incline to be easier on the shoulders as well.
Similarly, those that don't seem to get good chest stimulation from the flat bench press may be better off with incline presses, low incline presses, or dumbbell press variations. If you're trying to prioritize your shoulder development more so than your chest, you may even want to make an overhead press variation your primary focus.
All the aforementioned choices would be considered assistance exercises in powerlifting circles, but there's absolutely no reason that any of them couldn't be main lifts, too.
Some healthy guys with good builds for squatting can do heavy back squats to their hearts' content and get nothing but phenomenal leg development. Others find that no matter how much they hone their technique, their structure is such that their squats always look like a squat/good morning hybrid. Finally, some find that heavy back squats bug their lower back, knees, and/or shoulders, even when their form is spot on.
If you're in the first camp, then the back squat may very well be a great exercise for you. If you're in the latter two camps though, you're better off picking a different exercise to focus on to build up your legs.
For example, if you've worked on your squat form to ensure you're using good technique and still feel back squats more in your glutes and lower back than your quads, you may be better off switching to front squats or Bulgarian split squats as your primary quad builder and focus on getting really strong at them. If squats bother your lower back, you'd be better served switching to front squats, heavy single-leg work, or belt squats.
Finally, if squats bother your knees, you may find that switching to box squats, front box squats, or low handle trap-bar deadlifts/Dead-Squats feels better while still allowing you to thrash your quads.
If a previous shoulder injury makes putting a bar on your back uncomfortable, the standard advice is to put your hands way out wide by the plates, but that can screw up your form and make it tough to keep a tight upper back. Instead, try using a safety squat bar, switching to front squats, doing low handle trap-bar deadlifts, or doing heavy single-leg work with dumbbells.
The conventional deadlift is a great exercise to add slabs of muscle to your entire backside, but many guys don't have the mobility to pull from the floor with good technique, while others find that heavy conventional deadlifts piss off their lower back, even when form is good.
As much as I like conventional deadlifts, I rarely recommend conventional deadlifts to non-powerlifters because most people are better off doing trap-bar deadlifts or rack pulls.
It all comes down to risk versus reward. With conventional deadlifts, the rewards are very high, but so are the risks. With trap-bar deadlifts and rack pulls, the rewards are equally as high, only the risks are fewer and there's a much greater margin for error.
Many lifters consider upper body pulling to be accessory work, which is a mistake. Classifying something as accessory work or secondary work implies that it isn't as important. However, for most lifters, upper body pulling should be a high priority for staying healthy, getting strong, and building an aesthetic physique.
Often guys will focus on upper body pressing strength and then just tack on some pulling at the end of the workout, if they even bother to do any. This means that pulling work often gets half-assed or skipped. Instead, set strength goals for your pulling exercises, and don't be afraid to start your workouts with pulling rather than always doing it at the end when you're fatigued.
For powerfliters, the Big 3 never change. However, non-competitive lifters have more leeway for variety and rotating exercises, so your Big 3 can change as well.
You don't want to change your primary lifts too often because, after all, the whole point of having primary lifts is to give your program a sense of continuity and a way to measure overall progress. But changing your primary lifts every 6-8 weeks or so can be a good way to avoid plateaus and overuse injuries.
For example, maybe you focus your attention on trap-bar deadlifts for two months, then switch to front squats as your primary lower body focus for a time to give your lower back a break while continuing to crush your legs. Then after a phase with a front squatting emphasis, you can go back to trap-bar deadlifts, or move to a different compound lower body exercise as your main focus.