What profession should I chose?

Always, without exception: make your Main an Explorer (Prospector, Forester, Tailor)

Always. No exceptions.

As long as you can gather and provide mats (aka crafting materials, like ore and wood) there is always someone willing to craft whatever you need. (If not, join the Last Great Alliance on Arkenstone 😉 )
The Explorer is also a Tailor who provides light and medium armour.

If you start with 2 character slots

• If your Main uses heavy armour (champ, cappy, guard): roll an alt and make this an Armourer (Metalsmith, Tailor, Prospector). Don’t bother with the Tailor part, let your Main Explorer handle that.
  Or:
• If your Main uses light or medium armour: make the new alt a Tinker (Jeweller, Cook, Prospector) instead. Don’t bother with the cooking if you only have two character slots.

ALL your characters use jewellery; 6 pieces/level span.

ALL your characters wears some kind of armour; cloak + 6 pieces/level span.

Life in Lotro is so much easier if you are able to at least craft most of this yourself, with the hides/ore your Main Explorer gathers.

If you have 5 character slots

• Make #3 a Tinker/Armourer (the one you don’t have) – as long as at least one of your alts uses heavy armour you will benefit from the Metalsmith.
• Either fill up with more Explorers – ore is a hard currency in Lotro and you can trade it for whatever you need.
  Or:
• Get yourself a Historian (Scholar, Weaponsmith, Farmer) and an Armsman (Woodworker, Weaponsmith, Prospector). Let one of those handle your weapons, not both.

You now have the possibility to gather/farm all the mats you need to craft all the items you need.

If you have more than 5 character slots

4. Make #6 a Yeoman (Cook, Farmer, Tailor). A Yeoman is, by far, the easiest way to level cooking.
   You will always need some more of some crop, and with cooking and farming on the same alt that is easy to fix.
5. You can also roll a Woodsman (Woodworker, Farmer, Prospector), but if you are not planning on guilding your crafters (more on that here) it is much better to go with more Explorers. Because. Ore. Always collect ore.