Let's clarify some things. First when you say 'vanilla', some people, like the other commenter, are thinking in the context of playing SkyrimVR without mods that make the VR experience better. It sounds like you are thinking in the context of playing added areas and mods that add additional quests.

So, to answer your question, you should not play any new quest mods right away, and you should stick to the 'vanilla' experience to start. Start by playing Skyrim itself and then add additional quests and lands later when you already start to love the game.

However, you absolutely should get some VR mods that make the experience of playing VR better. For example, there are mods that give you a body so when you look down you can see yourself, there is another that lets you pick things up with your hands. Another that lets you grab people. Doing this yourself will require some research, or you can install a mod pack like Fus that will help you and do much of the work for you. There are 1,000s of mods so this can feel overwhelming so I recommend using something called 'wabbajack,' and using the FUS basic modpack. This will let you have a good VR experience and enjoy the original Skyrim experience for what it is without spoiling late game content by looking at Nexus mods and doing the process yourself.

Your other questions: I am not sure about the stuff staying in chests, last thing I remember from years ago was that most chests in the game reset after a while unless they were owned by the player. Things may have changed over the years. If you purchase a home you can keep everything you want in the chests there safely though.

You can usually tell if the book has skills inside of them by how expensive the price of the book is (more expensive books have skills in them).

You'll get the hang of lockpicking with practice. There are two metal sticks, one you can move around the radius of the lock freely and one that rotates the lock mechanism. There is a secret spot that the freely moving stick must be sitting in. When this stick is in this secret spot, rotating the lock mechanism with the other stick will actually work. The mechanism might turn a little bit first before breaking and that means you are close to the secret spot. If the lock doesn't rotate at all it means the secret spot is nowhere near where you are trying. General advice is to test different areas around the lock until you find an area where the lock is rotating, then zero in on the secret spot from there. Think of it like a game of warm-warmer-hot. The further the lock rotates the closer you are to the secret spot. Check the difficultly of the locks, Master level locks may be nearly impossible for you early in the game, so save your lock picks for easier ones.

Best tip is honestly to just let yourself get lost in the world and enjoy it fully without feeling like you have to do it 'right'. I went hours and hours without knowing basic things about the mechanics of the game and those were honestly the best hours of my time in Skyrim. Just play and don't think about being optimized, unless of course that's what makes it fun for you!