Just graduated a kid so have completed four years of cross-country schlepping. Initially, we debated about bins but ended up going with boxes that we checked as baggage. Good boxes, not overpacked (weight) and taped well will survive most anything. We did have some good-sized boxes that weighed near max limits.

My 1K baggage options were definitely the key to our doing this without extreme fees being imposed. At times, I would also upgrade my college kid, like I did to get him home from graduation - and this gave us extra baggage checking opportunities. The return trip after graduation in May was four boxes, two duffel bags, and carryons.

One bit of advice, if year-to-year storage is not available: each year, starting with Christmas break (if possible), have your student bring things home that they've realized they do not need to help minimize a packing/shipping crisis in the spring.

I should add that for freshman year, we bought as much as we could when we arrived in the area of college and did not ship things that could be purchased there. Most of our shipping adventures ended up occurring after that time.