If you get a 9th or 10th generation i5 laptop they will be fine for the job as they are proper quad core chips.
Good luck finding a portable battery that will power your mini ITX system for a 6hr school day in addition to a monitor, will be a huge pain to take between classes and to study session too haha. This can't be a real suggestion? No teacher is going to let you set that up on your desk.
I would suggest this laptop for your needs -
https://www.amazon.com/ASUS-VivoBook-i5-10210U-Windows-S433FA-DS51-WH/dp/B07YY11XL6/
If you compare the i5-10210U to the i7-8665U you can see it's better than the previous generation i7s (well, basically identical performance) so will be perfect for your schooling.
https://cpu.userbenchmark.com/Compare/Intel-Core-i7-8665U-vs-Intel-Core-i5-10210U/m740553vsm819403