Best international hard or soft ROLLING/SPINNING carry-on.

The bag I see recommended most often is the TravelPro MaxLite 5, which comes in several sizes and with either two or four wheels:
https://travelpro.com/search?q=maxlite+5&type=product&options%5Bprefix%5D=last
It's important to know the carry-on size limits for the specific airline(s) that your child is traveling with. While most transatlantic flights will allow the usual 22x14x9 bag, flights within Europe (especially on RyanAir, EasyJet, etc) often have strict size and weight limits for carry-on bags.
For the past nine years, including 7 months traveling throughout Europe, I have used this Osprey Ozone 2-wheeled roller bag:
https://www.outdoorgearlab.com/reviews/travel/carry-on-luggage/osprey-ozone-wheeled-22
They still make a version of this bag, but it's not as roomy or as light as the one I have. Volume to weight is the key ratio, IMO. If you can find a lightly used one on, e.g., Facebook Marketplace, you'll be getting a very good bag.

I'm one who has the Travel Lite TravelPro MaxLite 5 21-inch carry-on spinner (in blue), and I love it. I had the MaxLite 4 and gave that to my daughter when I bought the MaxLite 5, and it's wonderful.

It only weighs 5.4 lbs, which is much less than most other suitcases, it holds a lot, it's durable, it's expandable and it's just a great bag. I've carried it over cobblestones, and I'm able to toss it up in the overhead bin without straining myself.

I've never had it dinged by a gate agent, except in cases where I'm flying a small plane and they take all the roller bags and have you gate-check them. But otherwise, it's always made it onto flights when I do carry on, and that includes a lot of regional airlines. That said, I've never flown Ryanair or EasyJet, so I can't speak for them. I really like TravelPro, and particularly this bag. https://travelpro.com/collections/maxlite%C2%AE-5/products/maxlite%C2%AE-5-21-expandable-carry-on-spinner

The "best' in absolute terms or within a certain budget?

I have a strong preference for soft side spinners . They usually have external pockets which allow a lot more packing space. Most hard side cases do not have pockets. I have had great luck with TravelPro.

I also have the TravelPro MaxLite 5 21-inch carry-on spinner (navy blue) and love it!
And I recently got the compact version which is just a tiny bit shorter which fits some airlines overhead bins better.

While I don't check it, I do have the option to expand and check if heavier. I am usually not a fan of hardshell ones especially if in a small hotel room where harder to open bag clamshell style.

I’m now a dyed-in-the-wool Briggs & Riley aficionado. They’re not cheap, and they’re heavier than many other brands, but they’re well-designed, have lots of extra features, and are virtually indestructible. The “Global 21-inch Carry-On Expandable Spinner” can expand its depth, so it can carry more if you expand it (but then it won’t fit carry-on dimensions), or it can stay compact and meet carry-on sizing. if I’m coming home and have picked up things while traveling (souvenirs, coffee in Norway, shoes on sale in France), having that extra capacity has been helpful, even if they means I check it coming home, or if I’m not taking a plane yet but just don’t want to have to neatly pack everything so it’ll fit into the carry-on size at the moment. Everything from the materials, wheels, and even zippers is first-class quality. If anything ever needs repair, they have a lifetime guarantee to cover it. They have a range of colors in all their designs, too, if that’s important.

As far as a “traditional” suitcase, I’m so old that to me, “traditional” means something with a handle and no wheels - spinning or otherwise. Something like a Samsonite from the 1970’s, when they were made in Denver. Roller, and later, Spinner luggage is recent, new-fangled, and more “modern” than “traditional.” Of course, to a college-age person (and you, too michterra), any suitcase is going to have wheels, isn’t it? What did people do before wheels, or Osprey packs (another Colorado company)?

I took this suitcase on its virgin trip last month and really liked it a lot. I was looking for a lightweight spinner
and came up upon it after quite a bit of research. Even though it is only a couple of pounds lighter than most of the cases that I was looking at (it’s listed at 4.19 lbs), I felt it was considerably easier to lift up when packed fully. The weight may not be an issue for a college age person, but it was something that I was heavily considering. It went on sale before Christmas (I got it as a gift).

https://www.antler.com/products/lightest-expandable-carry-on-luggage-antler-green-soft-stripe-2

My son received my TravelPro. It’s a beautiful case, too, but is bigger and heavier. He really likes it. It has a pocket for your power supply, if that’s something of interest. I got it about 5-6 years ago, heavily marked down, during a holiday sale at Macy’s. It may be too long for some international carriers, though. We’ve only used it going to the UK and back (British Airways and United) and haven’t ever had a problem.

https://travelpro.com/collections/carry-on-luggage/products/platinum%C2%AE-elite-21-expandable-carry-on-spinner?variant=19629336756322

I also have a Travelpro (but it was built for Macys, and no longer sold); it's able to be a carryon but I check it. It's a beige/peachy color, which I love, so it's easy to see.

It's a hardsided 4 wheeled spinner, too. it's survived a mile walk from the bus stop to my hotel in Chamonix (and back), being checked w Air France, Air Canada, BA, AA, and train travel.

I'm pretty sure it's equivalent to this one - https://www.macys.com/shop/product/travelpro-walkabout-7-23-carry-on-spinner-created-for-macys?ID=20017100&swatchColor=Black#BRAND/Travelpro

Love my Away, it’s held up for nearly a decade and was wholly replaced hassle-free when I inquired about a part replacement, so I ended up getting two suitcases for the price of one. They come in great unique colors so I rarely have to check the luggage tag (I do anyway).

Travelpro Maxlite 5 are sold in both "compact" and "international" size configurations. The volume's about the same but achieved through differing dimensions. I don't recall that either fits a Ryanair cabin-item sizing bin. My main gripe with all the Maxlite 5 cases is the wheels are singlets and the hubs designed to minimise weight. I've read far too many reports of the wheels failing and thus can't consider them merely anecdotal outliers. I'd be wary if I were planning on using the bag more than very occasionally tipped-up on 2 wheels over rough cobbles.

The only rolling bags I own are the RS 2-wheelers, and only because I found them for roughly a third of RRP in mint condition. They're stored away in case I ever lose the ability to carry the RS backpack...hopefully that won't ever happen though.

I have the same Antler suitcase that Mustlovedogs added a link for. I used it this summer for the first time and loved it. I purchased the Antler compression cubes as well. It worked great for my two weeks in Scotland.

If I take a suitcase, it’s my favorite lipault here: cabin bag.

Overall Dimensions: 21.6"H x 13.8"L x 8.3"W
Weight: 4.8 lbs.
Volume: 36L

Also love TravelPro but when it comes to luggage I haven’t found anything that beats my Lippault cabin bag on weight.