First of all: Welcome.
Second of all: you're a lucky brat!
My very first recommendation is rather than just taking someone else's word for it (although that's good too), go to the library or bookstore and start perusing guide books for different places and get an idea for what appeals to YOU.
For example, I could tell you that Paris and Barcelona are absolutely wonderful-- and so will a lot of people-- but I also know at least 5 or 6 people who despised Paris and were bored with Barcelona.
After you have a general idea (read: a big list), start probing that further. But also don't limit yourself JUST to that: when you get over there you can pretty much do whatever you want! And with a 9-month time window, shit-- the sky's the limit, man.
Also, since you're Canadian, you can apply for a Working Holiday Visa for the UK. If you're planning to be gone for 3 months or more, I HIGHLY recommend getting some work over there for cash to spend on your travels. Being a US citizen (and not a student), I am seething with jealousy.
Hostels seem to be a popular working destination.
As far as budget goes, well, I'm not really EXACTLY sure how much you're going to want to bring but I would say that shooting for about $75/day CDN would be a good place to start. If you get work and your room/board is included (as it would be in a hostel), so much the better.
For what to bring: Well. Besides the essentials -- clothes, a few toiletries, passport, etc.-- I would say a camera would be the number one accessory. I prefer digital myself.
Also bring a book or music player of some sort for the plane and train/bus trips. And don't forget battery chargers for anything that needs it, rechargeable batteries (preferably NiMH), plug adapters and *possibly* voltage converters. If you can, try to get devices that have dual voltage so you can avoid the hassle of dealing with a voltage converter. North America runs on 110-120 volt, and Europe runs on 210-220. And remember that the UK & Ireland have different plugs than the rest of continental Europe (and they're ALL different from ours).
But plug adapters are dirt cheap-- don't worry about that.
I'll try to think of anything else I've forgotten or someone else will be along to add to the list.