luggage

My wife and I work as English teachers in Seoul, South Korea. This August, we will be returning to our home in the USA, but we’d like to take a detour through Europe on the way.

Here’s the problem: we’re not really sure what to do with all of our luggage while we’re hosteling and jetting around western European countries. We can’t leave it in Seoul, obviously, but we can’t take it with us on the European leg of our trip. Mailing (even via boatmail) is cost restrictive.
Is there some way to, say, fly into Rome but have our luggage forwarded to Paris and stored ‘til we complete our voyage?

First off,

Thank you to everyone who replied to my various threads, you have been a big help in organizing and planning our trip, and my and my travel partners are extremely grateful for that.

Now to our new dilemma!

We are pretty good about packing light, so size dimensions and weight shouldn’t pose a problem with carry-on (from either the U.S. to Amsterdam trip or the Ryan Air trip from Barcelona to Venice). The problem were having is with the items we feel we should/need to bring…these include nail clippers, razor, pocket knife.