I'm an "IT Professional" in my daytime gig. I'm in charge of outfitting my company with computers, and I've had to revamp/replace just about every machine in the place in the past 2 years. This is one of those things where there are a ton of correct answers. Unless you want to spend big bucks, let's stick to Windows machines.
It depends on what the kid is going to be doing. If it's taking notes, they are going to want something that gets going fast so they don't miss out on anything. Like others have said, that means a SSD and at least 6-8GB of RAM, and keep it updated. With Windows 10, if the PC isn't updated, it slows down considerably from my experience.
I'd be looking at 6th-7th gen Intel i3, i5, and i7 machines. They have been making the three of these for years now, and you have to be careful when selecting one. A newer 2-core i3 might outperform an older i7! A good resource to find out what's good is CPUBenchmark.net. The higher the benchmark score, the more horsepower under the hood.
If they are going to do anything that is graphic intensive, that means you are going to need a decent graphics processor, and machines with those cost north of $500 and closer to $1000 for good ones.
I also recommend a 1080 full HD display if you can swing it. It really makes a difference.
Size matters, too. Anything bigger than a 15" is going to be too much and portability and case/backpack selection will be down. I've gone from a 17", to a 15" and now to a 13" for my personal machine at home.
One annoying thing about a lot of new consumer machines is that access to components means completely disassembling the case. That includes the battery. Business laptops like Lenovo's Thinkpad series still have old-school component parts and easy access to drives and RAM.
Just about everything comes with massive amounts of bloatware. One good feature of Windows 10 that they now have a feature where you can ditch all non-stock apps in one fell swoop by resetting Windows through Windows Defender. It also makes a list of all the apps it uninstalls and drivers you might need to re-download.
This is the machine I'm running as my "daily driver": http://www.microcenter.com/product/475348/Pavilion_x360_Convertible_m3-u103dx_133_2-in-1_Laptop_Computer_Refurbished_-_Gold_and_Silver?ob=1
I love it. The screen is great, it has a backlit keyboard, and battery life is not horrible. It has a 7th gen i5, 8GB of RAM, and a 128gb SSD so it's lightning quick. I would recommend it. Another great option is an off-lease or refurbished Thinkpad with decent specs. They are built like tanks and are easily serviced.