Overall, I'm quite impressed but there are a few things that I would change.
The materials look amazing but there is a lighting difference between Avatars and Home which makes colors look differently. I picked what I assumed was purple, and it turned out to be blue in Home. Uniform lighting and color grading across all Oculus menus would be preferred or a selection of different lighting presets within Avatars.
Left/Right navigation buttons behave unexpected. Maybe it's just me but I would expect the right button to navigate a menu to the next item on the right side instead of moving the row of items to the right and thus my selection to the left. I get that you're mimicking touchscreen behaviour here, but when you're dealing with buttons, it's (at least for me) counter intuitive and inconsistent with other Oculus apps.
Here are a few things that I think would be nice additions:
The ability to save multiple configs as presets. This would be nice for people with shared PCs and to prepare different outfits for certain occasions. For example, I'd like to save a formal preset for occasions like poker and more casual ones for playing with friends.
A store for custom items. This is a big one for me - I think there is a ton of potential if you allow third parties to create their own faces, hairstyles, clothing, glasses and maybe even materials and sell it through the Oculus store like Playstation Home back in the day. I would jump on that immediately and make items. It's also simply an easy way for you to make money by taking a cut.
Profile pictures. I think it would be nice to be able to use an avatar as a profile picture, A novel way to do this would be via a camera that you can pick up and use to take a virtual selfie.
Normal map intensity slider for faces. This would be an easy way to control aging independent of the actual face shape.
A rear mirror. There is currently no way to check whether a hairstyle has a bun or not without neck gymnastics.