The most important decision you have to make in the game is which Supply cards to pick up in Towns and Forts and which ones to discard if you fail to ford a river. I've got a few ideas.
Ammo is always the first thing I get rid of. It can't save your life, and the best you can do is to trade it for a Food card if you're lucky enough to draw one of the two hunting Calamities in the deck. Never pick this one from the Shop.
Dead Oxen is a relatively rare condition, but if it shows up and you don't have an Oxen card, it's an instant failure for the whole party. It's a good idea to make sure the party has at least one of these cards available, maybe two.
A broken wagon is more common than dead oxen, but it can be mitigated by a die roll. Still, it's an instant failure if it comes up, so I try to keep at least two of these in the party's hands if possible.
Food and Clothes
Starvation and Extreme Cold are relatively uncommon Calamities, and they only affect a single party member. I give these about middling priority.
Medicine and Clean Water
There are many Calamities that can be solved with Medicine and Clean Water, but many of these Calamities aren't immediately life-threatening; the party can go a great distance before Measles or Unclean Water has any consequences. Moreover, there's more of them in the deck, and your party is likely to get a lot of them at the outset. It's a good idea to keep a few of them on hand, but they're probably the most likely to go if I need to make a sacrifice and I've already ditched my Ammo.