For a first toon I generally recommend Explorer as you can gather wood and ore and feed it back to other crafters (or sell/trade). Explorers are also tailors so you can make your own armor.
Woodsman are woodworkers so you could make your own instruments, but generally easier to get a new instrument crafted every 10 levels than a whole set of armor.
Tinker can make jewelry and again easier to get an instrument made than a whole set of jewelry...but the best jewelry as you level seems (to me) to be rewards from Pelagir runs... also includes cook, but then you need a toon to farm the mats needed to cook with.
Armsman can make weapons (and instruments if you can get processed wood) but a minstrel has one melee attack and after level 45 to 50 you are using a Legendary weapon so seems low priority to me.
Historian has Scholar who can make a few useful items like battle and warding lore scrolls, also weaponsmith but nothing compelling as far as I am concerned.
Yeoman includes cook and farmer so much more convenient than have to alt back and forth to get mats to cook with.....and there is still a market at endgame for High level foods
Armorsmith just seems like a waste since no use for heavy armor and the occasional shield or crafting tool can be gotten from others.
Since we no longer craft Legendary weapons a lot of crafting just seems low priority, but you can always sell logs/boards, Ore/ingots and Hide/Leather or send to your own lower level crafters.
Tinker can produce jewels. you have many slots for that and later you can craft the hope coins.
Historian can produce the scrolls you would like the have in battle. in addition you can craft colors, for your outfit :-)
Explorer is also good, harvest metal and wood and use the skins you get from the animals you kill. you can also craft your armor for the leveling part.
in addition it is easy to find someone for crafting, if you have the material.
Later it does not matter, except that you get easy mats, while questing.
cook looks good, but you need so much space, that is would be better to have that on an other toon. The cook can stay in the shire and only need cold coins for the mats (seeds).
My Minis are Explorer (level 140) and Historian (60) (and my Former Mini is Tinker (around 35), the job get replaced by my other Warden (60) that is the main Tinker.
I have 14 characters, 12 slots from when I originally played (although SSG couldn't recover my original characters and I'm having to re-level them) and two slots I got just for subscribing (I think). Noting that I', old and retired, I have lots of time available to play.
I have all classes, genders, races covered and a mix of crafting skills available, which is good since I can stick stuff in shared storage for other characters to use.
My female human minstrel uses forestry and woodworking so she can make her own instruments. Using the red trait line, drums are the best instruments for killing opponents. She makes her own.
There is a argument for making the profession of any first (main) character an Explorer. Of whatever class (or trait tree).
1. Gems, leather and scholar materials will drop from mob kills; wood and ores will not (as a general rule); ingredients for cooking are farmed, bought and most recently fished for. Mining will also provide some gems.
2. Low level alts can make high level crafted stuff - if they have the material.
So as long as your main character collects stuff you can - if you are so inclined - craft (pretty much) anything. (Few exception relate to craft guild membership - which alts could access - and a few faction related recipes.)
Yes it is possible at level 20 to get crafting materials of any craft level from the Woe of the Willow instance from the "box of crafting items" reward - and other instances / missions as your character progresses this will be a much slower process.
KEY QUESTION: do you need to worry about crafting when starting out? And there is a strong argument that the answer is no. Drops and quest rewards will carry you along if you follow the main story line / do the various zone quests. Which you can augment with gear acquired from mission tokens / faction tokens / marks.
Leveling is the key - you can focus on the crafting later. Which also points to selecting an Explorer - since you can collect wood and ores as you level and at some point in the future change your profession if you so want. And make alts to sort the mats and for when you need extra vault space. You can share things via your house chest (or shared storage). You can have your alts form a kin as welll so that done the line they can buy a kin house as well if you need even more storage.
SO WHY CRAFT? The main reason is that at / near end game you will want to have access to Food buffs (so Cooking) - but note that you can probably buy this on the auction house; hope tokens (jewelller) and battle/ward scrolls (scholar).
When it comes to crafted gear it can get you to the level you need to get better (raid) gear lets say. Not the only way to get "starter" stuff though and a lot of (non-crafted) gear you get these days is bound to account - so you can pass it down to lower level alts.
There have been times when crafted gear has been very good indeed (last time was probably when the cap was 100) and, as mentioned, crafting was more involved in Legendary items. The past is not the present though.
Disclaimer: I have all profesions covered with fully guilded characters. When I create a new alt though I don't bother making anything - you will out level any gear you make so quickly. Not even a need for food etc.
If you hit any "speed bumps" in certain zones do some missions to gain a level or two and then return.
I would argue that crafting is pretty important at all levels. Crafted gear (especially at the beginning) can be far superior to drops. Food and scrolls are important at all levels (assuming you are doing somewhat challenging content). I always eat food, read scrolls, and use tokens in group content. Best in slot jewelry can be obtained from Epic Battles starting at level 20, so you can almost say no to that profession (except for hope tokens).
Anyway, make a stable of crafters, or join friends that can fill in the gaps.
I would argue that crafting is pretty important at all levels. Crafted gear (especially at the beginning) can be far superior to drops. Food and scrolls are important at all levels (assuming you are doing somewhat challenging content). I always eat food, read scrolls, and use tokens in group content. Best in slot jewelry can be obtained from Epic Battles starting at level 20, so you can almost say no to that profession (except for hope tokens).
Anyway, make a stable of crafters, or join friends that can fill in the gaps.
A full set of crafters for your first character though - not an option.
Intersting point about Epic Battle naking jewelry somewhat unnecesary. And it is an option to get gear.
I wouldn't suggest focusing on "best in slot" though. And - and this is simply my opinion - I wouldn't bother with them at level 20. Yes they can offer very good gear - some of the newer areas e.g. Angle have very, very good gear however - but the epic battles and system a) have to be learnt b) get easier the more you do them - and acquire battle tree points c) would distract from landscape deed virtue points. Probably good to do them though from say level 85 to 105ish say - since they are fun and were a big part of the game once. After level 100 though - are they best in slot? Not sure they are - I did a quick run or Pel a few weeks ago but don't recall anything remotely close to Gundabad gear (or earlier).
Merely an opinion however. As I said crafting does have "a role" but I simply don't see it as a "significant role" whilct leveling especially whilst starting out.
Yeah, I can't speak to anything beyond Enedwaith, so I take your word on higher level Best in Slot stuff. Raid gear is still pretty important at low levels (better than crafted), but you need some good gear to beat the raids. Always the catch 22 in this game.
Anyway, a bit of context: I am a completionist Turtle Stone wearing weirdo, so take my advice with a bag of salt.