I took DD to the baby massage class at the local children's centre. She was prem and tiny, and after the first week I didn't feel like it was a good idea (class kept having to stop for me to pick up/comfort/feed her. So the tutor, bless her, came to my house for private lessons! For free! TBH though, we haven't really done it since.
I have only ever moisturised if she needed it. Actually, DH and I had a conversation earlier about this. She did have eczema, and doc prescribed hydrocortisone and moisturiser. It kept getting worse and worse. We went away and forgot the creams, and haven't creamed since, and we've only just realised that since not creaming she's had no dry skin whatsoever! So I'd say only worry about that if it occurs, then if it does, just treat the local area. The problem with moisturising, as you will know from your own skin, is that your skin becomes dependent on it.
If you want people to get you things 3 months plus you really need to tell them. We had so much stuff for prem/newborn that she didn't wear all of it, whereas we had to buy stuff (not much TBH) for when she was older.
As long as you have enough stuff for the first couple of weeks, you should be fine, as it will become apparent what you need. Also, don't be afraid to ask if your friends have children who have grown out of stuff. I've just lent loads of newborn equipment to a friend who is pregnant. They don't use it for very long. Our house is still stuffed with it! (We bought 2 lots of everything as we were expecting twins and DD1 was stillborn, so really had a lot of clothes in particular, plus 2 moses, 2 chairs etc...)
On that thought, where in the country are you? Want some stuff?
Do you know if you're having a boy or a girl?