Well then, welcome (back) to the game!

I personally found the most "noob friendly" class to be Magicka Nightblade. You have great self-healing AoE and single-target damage skills and your execute, and you get your light armor shield. Especially when starting a new char, you quickly get the Tri-Focus passive that lets you do AoE damage with a lightning staff for zero magicka cost (actually you restore magicka).

1.
You start out without CP, no matter what. But having a strong character is only one side of the medal. Knowing your class and skills, i.e. playing skill, is the other. So once you get re-acquainted with that, you're good to go for Normal dungeons. You can start with that as soon as you get your second weapon bar at level 15 I'd say.

Otherwise, please elaborate "competitive".

2.
Sorry, I only play on PC, so can't say anything about that.

3.
What role do you intend to play in PVE? For healer and tank, there's some combos that are better suited for the task than others. E.g. Imperial or Argonian DK for tank, Breton or Argonian Templar for healer. Wardens make good off-tanks or secondary healers in trials too.

For DD, no class is really "considered above average" compared to other classes. Maybe except for the Warden which is a bit sub-par. But a good player can do (equally) decent damage with any class/resource combination. It's more about finding your preferred playing style.

Do you prefer melee or ranged? Do you rather prefer to avoid damage by blocking and roll-dodging around, or mitigate damage through shields? Questions like that determine the recommended class.

For the record, you'll never be "max level with 0 CP", because you get 10 CP for free once your first character reaches level 50. Also you get maximum enlightenment, thus your first roughly 100 CP are earned very quickly.

To be "appealing" to groups, you primarily should be able to fulfill your role to a point that the dungeon run is smooth. Not necessarily turbo-fast, or immediately with speedrun, nodeath, hardmode, all that stuff, but smooth.

I.e. tank should taunt, survive, chain and CC adds, buff the group as good as possible. Healer should keep themselves and the group alive and buff as good as possible. DD should do decent damage and how to survive things the healer cannot compensate for. And everyone should know mechanics, so familiarize yourself with them on normal level before going vet. That's especially true for DLC dungeons.

To give you an example what makes you unattractive to groups: Just the other day as a DD I got into a group for vet Wayrest Sewers 1 (which was pledge that day). The healer had 15k health and got one-shot all the time by the simplest random boss attacks. Tank lost aggro repeatedly, and was unable to survive for more than 10 seconds without the healer. The second DD, even though they had 800+CP, must have had less than 10k DPS, since I did 70+% of the group's damage. You might want to avoid going into vet dungeons when you play like that. Take your time and train properly in normal dungeons.

Hmmm since this will probably be my only character, I would like a class that could be above average in all 3 PvE roles and be above average in PvP.
Maybe the warden is not THE class for me. Btw, I bought the ps4 version last night... a bit overwhelmed with all there is to do.

I'd strongly suggest to not try and put everything into one character. You'll end up with a char that does everything, but nothing really good.

Especially for DD, heal and tank you definitely should make multiple characters, otherwise you'll end up respeccing all over the place to switch roles (if you want to be above average). You need to set your attributes and CPs differently for the three roles.

Wardens are good in PvP because there you HAVE to be good at all roles. You need to be tanky so you don't die after two hits, can heal well because you need to rely on yourself in many occasions, and still do decent damage.

Wardens, especially magicka, currently lack the skills though to be good PvE DDs. Note that Zenimax can't make the Warden the "overall perfect class", otherwise it'd be serious pay-to-win, since it's a class you only get if you buy the Morrowind chapter.