Don't worry, I'll take pictures.

I actually want travel advice, because I've never flown before, much less been out of the country. The trip is part of my school's study abroad program which is coming up in like a month. We're going to land in Rome and be there for a night and a day, then we're going to Florence for half out stay and Assisi for the other half, and we'll stop in Venice for a day too.

We get back right before Christmas so I was planning on buying all my Christmas gifts there, so I have to pack smart. We get 1 checked bag that has a weight limit of 50 lbs, a carry-on and a personal. The weather's supposed to be cool, 40s and 50s, so I want to be sure to have enough warm clothes though, being a Minnesota native, I have a high-tolerance for cold weather so I don't want to be TOO warm. 

I'm mostly concerned about my suitcase (well actually my mom is more concerned about it than I am but yeah), the brand is "Advantage" and I'm not certain if it's sturdy enough to fly to Italy and back, and wondering if I should invest in something better. It works fine imo, but I wanted to be sure because when you're staying more than a month in a foreign country it would be terribly inconvenient to lose the majority of your luggage. 

Thoughts/suggestions/derogatory comments?