train travel in Italy

Trains from Milan to La Spezia run about once/hour. There is one departing at 12:10, yours at 13:10, and another at 14:05. Milano Centrale is a big station, but 40 minutes gives you lots of time to make the connection. Don't be surprised if the 13:10 train isn't even posted on the electronic boards until after you have arrived. To speed things up you could be standing at the door of your car with your luggage when the train pulls into Milano Centale so you are the first ones to get off.

This is encouraging.
We are traveling first class - will our luggage be with us or in a bin?

You are responsible for your own luggage - getting it on an off. You luggage will be where ever you put it. It is big you will have to put in the bin and if carry on size you can put it on the overhead rack. First class doesn't make any difference with regard to luggage.

Catherine, When you arrive at Milano Centrale, check the electronic board to find the number of your train and which track (Binario) it will be departing from. Sometimes this information isn't posted until about 30-minutes prior to departure, so if you don't see it right away just keep checking. The train number will be printed on your ticket (ie: IC-9171). All the tracks at Milano Centrale are in the same area, as it's a "terminating station" rather than a "pass through station" (ie: all trains roll-up to a dead end and then stop). It's often noisy and chaotic there. Be sure to watch your luggage! One other point to mention. If you need to use the WC during your stopover in Milan, there are some one floor down on the moving sidewalk. It's a "pay-per-use" facility, so keep some Euro coins at hand. Are you staying in La Spezia or continuing to one of the towns in the Cinque Terre? Happy travels!

You will have plenty of time; just follow the advice that others have given you here. I just want to add that Milan Central Station is as big, crowded, and busy as an airport. It's on several levels, but they are well labeled, and their are inclined moving sidewalks as well as elevators to take you from one level to another (no need to drag your luggage up or down stairs). It didn't bother me, but my friend was a bit freaked out at the size and movement - just be prepared. And, for some reason, I've seen several people freak out when their train is listed, but no track is posted yet (even when their train isn't leaving for over an hour). Don't panic - just keep checking, and your track will be posted sooner or later (remember, no one can board until the track is posted, and you have a reserved seat). As for luggage: you lug it. Be sure you can handle carrying it, getting it quickly on and off a train (in stations smaller than Milan, you only stop for a few minutes), and putting it up on a luggage rack (possibly overhead). If you can't, pare down what are bringing, or you will be miserable.

Thanks to all of you for the tips on train travel and luggage.
We will be using luggage that is designed for air travel carry on so I'm hoping it will be fine. I had read on another thread about putting luggage in a bin or on a rack, so that was what made me wonder if we'd have to retrieve our bags.

If you only have a small carry on type bag, there will be room at your train seat (above or next to you) for your luggage. Otherwise, there is usually baggage storage at the ends of the car near the exit.