There is a school of thought to have a small diameter peep for greater accuracy, but I am not a tournament shooter, I am a hunter so I have a large diameter peep (don't remember what make) on my bow.  It is set up so that I frame my entire round sight with it and not just an individual pin.  I don't use a hose and it stays in place, but I had to shoot it a while to get the stretch out of the string so it wouldn't rotate past where I wanted it.

Peeps are inexpensive and a bow shop should be able to install it for a small amount.  I get a larger one to take advantage of the last light.  Sunset was 6:17 pm the other night and at 6:45 I could still make out my pins through my peep.

Your pep sight should not be moving around.  Make sure it is fixed properly, right where it needs to be. Then, when you practice, it almost becomes second nature to put it to your cheek, and look for your pins to aim.  It is almost like you are not paying attention to the peep, as long as you always anchor that release to the exact same spot every time.

I use a 3/16" G5 Meta peep they are blue in color so you can pick it up quick. At least I can. Sounds like you need to serve your peep in to keep it from moving. Youtube has some good info on doing things like that.

I use a 1/4 in peep, Dont remeber what brand, but like others said your peep shouldnt be moving around, take it into a shop and have them fix that by serving it. When i first started to shoot i would practice drawing my bow back with my eyes closed and when i opened my eyes it would be lined up with my aiming eye. now its jus second nature and at the same point everytime. my peep hasnt moved since i put it in.