When you’re changing lenses, you want to be careful with your camera and lens, making sure you don’t drop them, but also making sure that the environment you’re in is okay. First of all, make sure you’re not in an environment that has dust floating around that will get in the body or on the lens.
When you take the lens off, point the exposed mirror or sensor down, along with the back of the lens. Gravity pulls dust down, so this should make the least amount of dust enter the camera and the back of the lens. Some people don’t care about the caps, but I always use both of them. I always get the new lens on first though. As soon as it’s locked on, I will put the camera down and put the caps on the old lens. Of course, if you have a PA, you can easily have them trade lenses with you and place the cap on the old lens while you put the new lens on the body.
Every few lens changes, I use a lens bulb to blow dust off the sensor.
It is very important to get as little dust in the body and lens as possible but if you have a mirror down on the body, dust getting on it will be much better than if you get dust on a bare sensor. It’s much less nerve racking to clean a mirror and it won’t ruin your shot if you shoot with dust on the mirror. Though, that obviously requires a DSLR, it won’t work with a mirrorless camera.
If you have the camera on a tripod, you could tilt the camera down and change the lens or just swap them fast.
If I have to make any sacrifices while changing lenses, it will be for the lens to get dust on it because I’m more confident in cleaning lenses than sensors. If there is something on my sensor and it doesn’t come off with a lens bulb, I will send it in for professional cleaning. It’s better to be safe with this kind of thing.