Remember that you will have to tote your OWN LUGGAGE, so the pieces you take should be manageable for you.

One large bag

44 lbs should be your heaviest target weight.  If you overpack, the airline might make you take things out, and then you'll have to carry more with you!
WHEELS are highly recommended.
Something expandable is also a good idea:  room for souvenirs

Small bags

Students will be provided with Travel Selections bookbags--good quality, not geeky-looking
A second carry-on bag should be OK and long as it still can be put in overhead compartments or under seats
Should contain toiletries and a few clothes (enough for a day) in case the larger bag is delayed or lost!!!
Should also contain important papers, documents, meds, etc.

Extra Bags on the way back

You might bring/buy an extra bag and maybe share with a friend.
Smaller bags are always easier.
Depending on the airlines and the size /weight of the bag, you might have to check an extra bag on the way home.

Marking

Make sure each of your bags is CLEARLY marked with your name and address. 
The company will send us brightly colored tags for all checked bags.
I also recommend a brightly colored ribbon of some kind for easy identification.