The Hip-Thrust is a research-proven exercise for greater glute activation than squats or deadlifts with minimal spinal stress. If you have tight hips, weak glutes or knee pain, then this exercise is the best place to start.
It can be done on the floor but the range of motion is limited. The shoulders-elevated hip-thrust increases quad contribution. The feet-elevated hip-thrust increases hamstring engagement. Once you can easily do 20 reps on both legs, progress to the single-legged variation. If you notice any imbalances between sides, do 2-3 sets on the weak side for every set you do on the strong side.
I highly recommend adding a mini-band above the knees to maximize hip development. You can also add band resistance around your hips or place a weight on your lap, though I prefer to keep squeezing out better form & technique with my bodyweight.