One quick point. I am not saying these are absolutely necessary skills for post-collapse, nor am I saying they are the only ones worth considering. It is up to each team to decide upon it’s own optimised load-out. This is simply the team I would strive to prepare.
This includes food gatherers. Botanists have an extensive knowledge of plants and their uses. They can be used either as food-gatherers or rudimentary medics.
Another obvious one. Blacksmiths are responsible for the maintenance and upkeep of the groups weapons. This skill-set includes bowyers, fletchers, armourers and gun-smiths. Their pack will contain the basics of their craft, including various hammers, tongs, planes, saws or axes for wood-gathering, a small set of bellows and a quantity of raw metal, wood, hides and other furnishings for weapons. The will also be responsible for keeping a stock of spares for the groups weapons, as well as sourcing material whilst on the move.
As well as the groups weapons, they will be responsible for armouring the group, and should have knowledge of various skills used there-in, such as leather-working, lacquering, ring-mail construction and clothing construction.