Which one of these pieces of equipment is the most important in helping you to build muscle?
The answer is: none of them. The most important piece of requirement you should be focusing on is your ... bed.
Most muscle building takes place when we're sleeping. Yes, you can stimulate muscle growth during your workouts. But it's during the actual rest process at night that you stimulate muscle growth. Failing to get a good night's sleep can actually seriously limit your ability to build muscle. Even the best workout can be completely undone by not getting this right. I typically get between 9-11 hours of sleep every night. 10 hours is my sweet spot. I wake up whenever my body tells me to. I feel good and well rested when I get up.
If you feel fatigued or not at full strength during your workouts, then you're probably not getting enough sleep at night. However, if you feel rested, even after as few as 6 hours of sleep, then there's probably no need to adjust that to meet some arbitrary "8 hours" ideal. It helps if you can sleep in a dark and cool room and if you maintain regular hours of hitting the hay every night. The bottom line is to get enough sleep every night so that you wake up feeling fresh and able to perform your daily duties with full concentration and motivation.
Hope you're having a wonderful day!