will luggage make it?

That is nearly impossible answer. About 99% of the bags make it just fine. However, if you have a couple of tight connections who knows. Bags make it off a plane in about the same time as a plane in the US - in the range of 20 to 30 minutes. There is no set answer for what you are asking.

The risk of your luggage being lost on a single flight is small, but the consequences could be severe if you are not going to be in the same place for several days. The risk increases exponentially each time you change planes. That, more than saving a few dollars, is why a lot of people use carry-on only and do not check luggage.

My experience is that it varies by airline. For example, going through Heathrow on AA or BA and having a connection, lowers your odds of getting your luggage dramatically. CDG can also be a problem if ground supports decides to strike or take a break. many of my colleagues use AA from DFW through ORD, and things just "happen" when they change in Heathrow, and we can spend the balance of a trip chasing down baggage.
AMS, Brussels, MAN(for me) seem to do a better job of getting your luggage to you than the others.

Just a suggestion, do as Rick suggests and carry on everything. You can pack 7 days worth of clothing into a wheelie that will fit in an overhead bin plus you can take one smaller bag for under your seat. We travel 30 days at a time this way and spend just a couple of hours on day 4 or 5 doing laundry. Not only does this give us a break but we get to chat with other travelers or the locals and that is part of the fun of traveling. Also by traveling light you drop all the angst of worrying about lost luggage.

It depends on the connections and whether or not there are delays. I did a trip with my parents that involved a flight from Madison to St. Louis to London Gatwick to Edinburgh to Kirkwall via Inverness. Everything arrived. Our travel had all what is sometimes referred to as "legal" connections. These are connections that the airlines believe are sufficient. We were traveling with partner airlines which improved the odds of things going well for us. Nevertheless, it's always wise to carry on some basics in case disaster strikes. Pam

Arlene, I'm assuming you're using "code share" flights, so all your bags will be checked through to final destination? Could you provide some further details on the flights you'll be taking? I may have some additional comments based on my experiences last year.

Be sure ALL of your luggage has a large sheet of paper INSIDE with your pertinent info - name, flight number/date/airline, your travel itinerary, a phone number and email you can be reached at, and perhaps the phone number of your first hotel. Probably the vast majority of luggage that's lost is due to outer tags being torn off; have your info inside. I say to put this in your carry-ons also because you never know when checking everything might be required, or perhaps you get separated from your carry-ons.

In all our travels we have only had luggage lost once. It caught up with us a few days later. have your ultimate destination address inside the luggage as suggested above. carry some emergency clothing in your carryon.
(our greatest inconvenience was underwear)

Do what Brian says. I always bring a change of clothes in my carry-on, just in case. I've had to use it on more than one occasion. I'd also check the lost luggage policies for the airline(s) you're flying. Some have policies that if your luggage doesn't make it after a period of time, they'll reimburse you a portion of the cost for buying new stuff, usually around 50%.

Most travel insurance policies include lost luggage coverage. Then if your stuff is lost, you can have some fun clothes-shopping in Palermo, knowing you'll get reimbursed. And you can go back home to Naples looking like a real Sicilian. :)

A related question. When putting your itinerary in your bag, what part of the bag? Do you put it in one of the outside pockets? Or in the locked portion? If the locked portion (TSA lock), how does one get in to get it. I know, this is a stupid question, but I thought I would ask.

There are a lot of good tips here: https://www.worldtravelers.org/lost_luggage.asp

How long is your trip? I strongly suggest carrying on your luggage. If you follow Rick's packing list, you can easily get by with a carryon-size suitcase, a backpack, and a day bag. If the airline(s) only allow 2 carry-on bags, stuff your day bag into your backpack. On a trip to Europe a few years ago, my checked luggage missed the flight from Philadelphia to Manchester, England and I didn't get it back until 2 weeks later, on the last night of the trip. Ever since, I do my damnedest to carry on my luggage. If I have to check a bag, I divide up my clothes between the checked bag and my carryon just in case.

I've never had luggage permently lost, but delayed if the luggage didn't make our flight. And I agree with previous posters that the more connections you have increases the odds. If you are traveling and staying in one place, a minor inconvenience, but a trip to Europe could mean your luggage might never catch up wtih you. If we do check bags, I make certain our carry ons have a change of clothes(including underwear) and other essentials for the trip. So worst case scenario, you can alternate between wearing and washing every day.