College admin here and a former college dad.
I'd recommend a small and lightweight laptop (MacBook Air, Surface Pro, etc.) as your base unit. You will be carrying it
everywhere so portability is key. Don't cheap out on 8GB RAM, but no need to go crazy either. Most importantly, do get a 27" monitor, keyboard, and mouse/trackpad for the dorm/apt for writing. When writing, you need space for several windows on the screen at the same time. Even as a finance major, you will be doing a LOT of writing.
I'd not recommend an iPad - for now. The process of taking handwritten notes and then rewriting them/reorganizing them is one of the most effective ways to study. If after a semester or two you feel an iPad would be helpful, then go for it, but don't feel you need it immediately.
The Apple education discount and back-to-school promotion are almost always less expensive than purchasing refurbished, so go that route and buy new. Get AppleCare (or similar). If something goes wrong, you need it fixed ASAP.
As for watching YouTube or whatever, I'm not sure size matters that much. There will also be someplace where you watch stuff with others on a larger screen when needed. Again, I'd prioritize portability and battery life. IMO, the choice between a 13" or 15" is more about your writing style than viewing style.
iOS vs Windows is a decision you will need to assess. Most colleges ensure any required apps work on both platforms - but your school may be different. I see plenty of Macs in the business school, but it is a Windows-orientated major. I guarantee there will be at least one scraggly bearded guy in there with some Unix distro as well
. As many have said above, call the department and ask if they have a recommendation. Ask the advisors and other office staff. They know all the ins and outs and are usually super easy to talk with.
Most importantly, study hard and enjoy!
[Edit to add. Good, comfortable, noise-canceling headphones are absolutely needed!]