"In weightlifting, the bench press is one of the most effective chest exercises, and a common gauge of progress"
No. Just..... no.
First of all, there is no bench press in weightlifting. In fact, weightlifters explcitly AVOID that lift because it ends up limiting shoulder mobility and interfering with the musclulature used in the competition lifts.
It's not the most effective chest exercise, and only to the skips leg day crowd is it any kind of meaningful benchmark.
The Bench Press did have a lauded position as the upper body squat in terms of upper body development, when it was first introduced and developed. The folks who tried to think of physical culture realized that there was pressing upwards, and pulling towards the back (the initial part of most lifts at the time) but little corresponding movement, a pushing movement perpendicular to the body. It turns out that the bench press works many upper body muscles: primarily the triceps and deltoids, but also the trapezius, latissimus dorsi, and to a lesser extent the chest muscles. It is possible to use the chest muscles to assist the lift, and with heavy enough weight the chest does develop quite nicely. But the function of the pectoral muscles is to pull the arm across the body, not press outwards.
In fact, the potential for injury because of stress on much smaller muscles like the ones around the rotator cuff have led a lot of more modern bodybuilders to do dumbbell presses, chest flyes and the pec deck, a machine which forces the user to bring both arms across the body, under load.
There is a significant amount of "bro-science" around the bench press, leading to people doing things like putting their feet up on the bench to isolate the chest muscles, which is dangerous and stupid. The other idiocy around the bench press involves the idea that incline presses work the "upper" chest, decline presses work the "lower" chest, and flyes work the "inner" chest. This is absolutely not borne out by any study of the contractions of the muscles involved. Also, the folks that decide they want more weight on the bar than they can handle to "impress" people, grabbing a bar and letting it fall only six or so inches rather than to the chest - are doing nothing more than triceps lockouts, working nothing but their triceps.
And the stupidest bro-science gym move to do - with the biggest source of injury - is to hold the elbows out at a 90 degree angle during the lift, to "isolate the pecs". What you are doing is inviting front deltoid damage and is the leading cause of people having to abandon the bench press entirely due to shoulder pain.
To properly execute the lift, you put your feet on the floor, and keep them rock solid. you bunch up your shoulders, pinching your shoulder blades together as if someone just hit you in the upper back This gives you a stable base to press from. You unrack the bar, with your elbows at your sides. You bring the bar down to touch your chest, momentary pause, and then press it back out, using your entire body to do so.
Banging the weight off your chest, using your sternum as a springboard is not only a sign of weakness but a vector for serious injury. Bringing your ass off the bench to press the weight out is a huge flag suggesting you're lifting more than you're actually capable of doing.
Some people do what's referred to as a reverse grip bench press: meaning that the palms are facing you during the lift. This should be done at least once with the bar to show you proper pressing technique, as it is impossible to do so and flare the arms out. But doing this with heavy weight is practically an invitation to be guillotined by the barbell when it slips out of your hands.
Doing a closer grip bench press transfers more stress to the triceps, making it ideal for gaining strength in the top part of the bench.
Needless to say, NEVER bench press heavy weights solo. Ever. People have died from not having the strength to lock the weight out and having the weight rest on the chest or worse the neck, leading to the person being rapidly unable to breathe and dying of suffocation and pressing injury. For this reason a lot of people train the lift in a rack, with "pins" set on each side slightly higher than chest level with the back absolutely flat on the bench, meaning that they don't interrupt a proper lift but the lifter can lie flat on the bench and shimmy out from underneath. Your spotter can either provide additional lift for you both to press out and rerack the weight, or the spotter can rapidly remove the collars on the barbell and remove weight plates from each side rapidly enough to allow the lifter to press out the empty bar.
Never bench press without collars on the barbell. If you somehow press up crooked and half your weight slides off one end, you're not likely to be able to control the barbell suddenly flipping over and out of your hands like a trebuchet, a danger to you and just about everyone nearby.
Don't bench press on a Smith machine - which is a barbell on "rails". Sure it's easier because the bar doesn't weigh anything (it's counterweighted) but it forces you to press in an unnatural plane and can cause a lot of joint injury over time.
Chalk up, wrap your wrists and go for it. But real men care about the numbers on their squats.