Hand placement largely depends on comfort (or ability) and whether you have a particular focus to training. Close grip means more tricep work and less demands on wrist mobility in terms of radial deviation. The wider the grip, the more radial deviation your wrists undergo, but at the same time less tricep involvement which leaves the pecs to do more of the work. Typically hands just outside shoulder width is a good starting position, it allows the glenohumeral (true shoulder) joint to operate at a fairly natural angle, without over-complicating the actual movement.
I personally feel the larger range worked the better, but this may come at the cost of how heavy you can lift. From a functional viewpoint, ability to generate power under a wider range of joint angles is more useful. If you’ve fallen and have to push yourself off the floor, you need to be stronger than gravity at all ranges or you’ll be left floundering. In terms of training heavy, we know mid-range movements typically give us the most power, so you’ll see some teeth grinding grunters at the gym (myself included) that prefer to work in shorter ranges. Either way, your body adapts to the demand you place on it so it’s helpful to incorporate a variety of training challenges.
Torso posture and foot placement tend to be under contention too. How much to arch? Where do the feet go? On tip toes or push through heels? I normally advocate a neutral spine, that’s head, thoracic spine, and glutes firmly planted on the bench. Some arching may be needed for intraabdominal pressure and overall stability, but for regular lifters engaging your glutes and core will automatically lift your lower back off the bench, anything more is unnecessary. Yes, you can lift heavier with a bigger arch, but you’ve also changed the angle of the push to be less horizontal and more decline.
Foot position may seem negligible for most beginners, but it does play a big role. Less commonly seen these days is feet on bench. This eliminates any possibly back arching, and makes it far less stable, but isolates the chest and requires more upper body balance and coordination. The other end is toes on ground, knees bent to get your feet as close in line with your bum as you can. The drive is quad dominant, pushing toes into the ground, but there’s a tendency to lift your bum off the bench and over arch your back. I generally start people off with feet on ground, knees at 90 degrees and pushing through the heels. This places emphasis on overall balance and control of the whole body.
What does it activate?
When performed as intended, the bench press, like the other primary lifts should utilise the whole body. The prime movers moving the bar up and down however, are the pecs and triceps. How much you flare your elbows will determine how much you involve your anterior delts. But, the whole shoulder girdle will either contribute to the lift or help stabilise the region.
Besides the feet up option as mentioned, the lower body works by counterbalancing the forces in the upper body. Pushing into the ground in turn pushes your chest back and up into the bar which helps with the push.