I am not skilled at any craft activities, but I do own a whole bunch of quivers. I generally prefer leather due primarily to the nostalgic aspect. Both soft and stiff leather have certain desirable traits.
If you are stalking through the forest, it would be advisable to consider one of lighter leather that collapses against your back as it cuts down on noise. If you hunt from a stand, the large, stiff quiver allows you to carry a lot of stuff, and the noise factor is less important. However, it is entirely possible to be stealthy using a stiff leather quiver. Just remember that if your arrows are rattling around, you are moving too fast.
When using my primitive gear I also like a woven basket quiver. Mine is totally plain, but some of them are quite attractive. They tend to be noisy unless you take special effort to reduce noise.
You will eventually find that you want multiple quivers, especially one that covers your fletching in wet weather. That is not a big factor for me 'cause I don't hunt in the rain, but it is a useful consideration.