I work in logistics, engine grad + SCM spec. and worked in aerospace procurement for a bit.

Qualities they look out for is being analytical/logical, ablility to think on your feet and very good with numbers (esp. financials).
Of course you can theorize your SCM knowledge (Econ. of scale, EOQ, JIT, bla bla.) and they might take the bait. Depends on the industry and function.
Also, being able to talk to articulate high level people (and laugh at their lousy jokes) and lower level blue collar types, will help a lot.

Apply for an operations function, meaning those jobs which let you deal with the inventory day-in-day-out, slog it out and learn like hell for a few years when you're young.
It will steer you towards a well-rounded thinking, as operations is the backbone of logistics.