An extra inventory slot is very necessary for survival, especially if you like lot's of guns.
Agile, Light Eater, and Awake.Edit
These should go without saying. Agile is needed to help not get hit, and zombies don't suffer from hunger or exhaustion, while you do, so do everything you can to prevent it.
Carpentry, Hardy, Strong, Tough, Firearms, and High Stamina.Edit
Nice bonuses, Carpentry and Hardy 1 are a little more important compared to the rest, so get them first. Strong and High Stamina are for melee while Firearms is for, well, firearms.
Medic, Bows, Light Sleeper, and Martial Arts.Edit
Mostly useless skills here, as bows' ammo is rare later as NO-ONE spawns with it. Medic is the most important here, though that ain't saying much. Martial arts is useless as at level 3 it only has a +3 damage boost, compared to the big hammer's +8.
- Martial Arts can become important later on once it's maxed. It gives you +9 attack (Higher than any current melee weapon.) and +3 damage along with an extra inventory slot or two for ammo or food. It's also much more stamina effiecient and reliable than using weapons. Big Hammer only gets 3.75-5.625 attacks before 0 stamina and max Martial Arts gives you 6-9 attacks. So, don't pass up the chance to grab it once you have the higher tier skills maxed. - Bananamartyr
This deserves it's own tier, as it depends what your going for. Going alone is less complicated, and you have less mouths to feed, but another person is basicly another 7-10 slots of capacity and/or a nice helpful fighter. Whether it's above Tier 1 or below Tier 4 is all up to your playing style.