I like bow quivers for carrying arrows to and from my tree stand. I want one that quickly detaches as soon as I get set in the stand so I can take it off and hang or tie it to a limb. I prefer the bow unencumbered while in the tree and not having to worry about arrows (especially fletching) bumping things as I prepare to take a shot. I've used bow quivers that stay on the bow in which case I practice with the quiver and arrows in place.
I prefer quivers that fit in the riser inserts or on quick detach devices under limb bolts.
The most convenient bow quiver (for quick detach) I've used is the new ArrowWeb by Mathews. This quiver (made for compounds) uses a special, circular bracket attached to two riser inserts (like a Kwikee quiver uses). You simply twist the quiver on or off. They come in 3, 5, and 7 arrow versions. Of course you can get a Kwikee, Bobcat or Lynx that works in much the same way (two closely spaced insert holes) for about 1/3rd the cost of the Mathews. I have the 5-arrow Arrowweb on "The Stick" recurve I hunted with this year. It doesn't feel as "traditional" since it is all metal and plastic.
I'm not a fan of the ones that have bulky brackets that slip over the bow limbs. I haven't used the strap on type but I have one coming in a bow sell/trade from a Trad Ganger tomorrow. It is a Great Northern. I have two other Great Northerns that I really like.
I have a back quiver, (Catquiver) that I bought for hunts that involve miles of walking (such as elk in the west). This one is mostly for carrying extra arrows besides those that would be in my bow quiver.
I've used hip quivers (a long time ago). They keep your bow clean of extra weight, potential noise, and flash. However, I hunt areas with interior fences and brush. I was constantly hanging the quiver up on "stuff" -- I even lost an arrow or two from this quiver -- pulled out by brush.
I bought my son a recurve for his birthday. I put a riser insert-mounted Thunderhorn on that bow for him. So you can see what I like -- I wouldn't put something other than my recommendation on my son's bow.
Whatever quiver you get, if it uses rubber grabbers, make sure the grabbers fit your arrows. Lots of grabbers are for "fat" arrows and many of today's carbon arrows are "skinny". You can get replacement grabbers.