I don’t play an archer, but I do habitually monster as them.
Having a buckler, a one-handed weapon and heavy armour means that you can always default to heavy infantry.
Having lighter armour means you can whoop around better as a scout or messenger in between shooting people.
Scavenge arrows, SAFETY CHECK EACH ONE, and then stick them in your quiver. I have gone out as a monster with 0 arrows and picked them up as I went. I recommend either ignoring EDIT: Fibreglass arrows or wearing gloves, as the splinters from those are horrible.
Since you’re near the back anyway, you’re not taking someone out of the front line to go and fix problems. Chirurgeon and possibly Physick are nice backup plans for if you run out of arrows. Putting one of your people back into the fight for sure is better than probably taking down one of theirs, most of the time.
Apothecary is not a skill I’d recommend because it doesn’t do anything interesting. It lets you turn Thing A into Thing B but since you can use it an unlimited amount, someone else can always do it.
Artisan’s a better pick, as each Artisan only has 3 months of craft time, meaning your time is valuable. There are plenty of good archer items. +1 Hit heavy (you’re a priority target for arrows), self limb fix (same reason), a Cleave sidearm for if you get rushed, etc.
Short-sleeved chainmaille (A haubergeon) doesn’t interfere with your draw, as chain moves with you and you won’t have it on the lower arms to snag. Plate will restrict your movement more, unless you have a crazy-expensive custom set. Chain’s also cheaper and less bulky. You can also shoot fine with just a breastplate. Even if that’s the only heavy armour you wear, you can have +2 Hits from Light Armour under it and not fall over to being shot in the chest. Heavy is nice because you know you can take a shot from an enemy archer, but you’ll probably drop them.
Magician and Battlemage will suck up all your points and mean that you will need to get hold of an Enchantment or Mage Implement of “You know this spell”. It will mean you have some hits, but they won’t help if you’re shot in the chest. Unarmoured isn’t as bad if you’re far enough back your main problem is arrows which instadrop you anyway. Try and get an extra hit on you in case of close combat or leg shots, there’s rituals and potions for this.
You can also decide “Archery is my battle skill, magic is my off-battlefield one” Buy Marksman, Magician, Lore 1. Buy Lore 2 with your extra XP from your first event. Wear armour to battle, it is Big and Clever.
Hero Points, Unstoppable, Cleave is a nice 4 point spend as you can wear Medium armour to cleave proof your chest, and if you have to, sling up your bow and go shanking. People don’t always expect the archer to draw a sword and cut their leg off. If you’re out of arrows, having a backup plan is handy.