Those are some big, open questions!
You, and every new player, are in a Catch-22.
The class that will suit you best is the class you will like most. This is because every class is basically capable of doing everything solo that can be done solo. But you will be much more competent with a class you enjoy, because you’ll be happier to play it, and will learn more about it.
But you don’t know what class you will like most, and you can’t even begin to find out until level 100, because classes do not have their full toolkits till then. If you have bought BfA, you can use a Level 110 Trial to get some kind of sense of a class, but honestly I’m not sure a really new player can make enough sense of being dropped into a 110. You’re more likely to be just confused. It’s worth a shot if you have one, though.
If you want to heal at all, ever, Mage is out, because Mage has no healing at all.
Between Balance/Resto Druid and Elemental/Resto Shaman (the ranged DPS and healing specs of the other two) I would personally pick Druid, and judging from the statistics, so would most other people.
But of course, I have no idea what you might like.
The nearest you can get without putting in a lot of hours on both is to hit YouTube, and check out videos of these specs. Unfortunately, these will mostly be advanced guides for competitive group play at 120, but if you look around a bit, you might find something you can relate to.
One thing I should say is that Druid has a tank spec. No, you may not want to tank groups, but having a tank spec available when you need it gives you a HUGE advantage in doing hard solo quests or Rares, without having to rely on other people to help you.
Server … for casual, slow, solo it won’t matter all that much. Alliance or Horde makes a BIG difference. If you want to get in with a bunch of PvP (but that’s not slow and solo) then that would make a difference as well.
I assume Alliance, since that’s what you’re posting on.
If you want a really quiet - dead, even - almost completely solo experience like you’re the only person playing the game, Earthen Ring or Moonglade are very quiet RP servers.
Personally, if I was new, I’d go Argent Dawn. Also an RP server, but a big one. You will see lots of people around, many talking and doing RP, but it’s all very friendly and you can still play at your own pace, with all the trading amenities of a large realm. Or you can go to mainline crowded servers like Silvermoon or Ravencrest (where you are at the moment) for the maximum opportunities for group play when you hit 120.
RP (Role Play) servers are the same as any other server, but your name must not be jarring (like RocketMan or IEatYUrFace), and you must not disrupt people chatting in RP or their events.