As someone who builds computers as a job, I get asked this a lot. The answer for me is always pretty simple: Don't buy a laptop with a hard drive, make sure it's got an SSD.
The issue simply isn't that "macs are better" because they do the same stuff it's just that one has a really nice casing around it and you pay an extra £300 for it. Not worth it tbh.
Hard drive systems will slow down with time, it's inevitable and SSD systems do not and are always super quick (starts up in under 30 secs guaranteed). RAM isn't that crucial as well, Windows copes fine on as little as 2GB of ram and (but OSX (mac) only copes well with 8 gigs)
If you like white, I've found the perf laptop:
http://www.pcworld.co.uk/gbuk/computing/laptops/laptops/acer-aspire-v3-371-13-3-laptop-white-10029103-pdt.htmlIt's got a great processor, graphics and it'll start up and run super-quick. The only drawback with having an SSD is that the capacity isn't that grest (note the 120GB space) However, this is plenty for your apps and music etc. There's plenty of budget left for something like a 1TB external hard drive. If you have a large movie collection you might want to get one because the chances are that you won't be able to fit your entire collection in 120GB.
If you're after something to take notes on, may I suggest something like a Surface 3. It's power won't knock your socks off but it's ingenious design will, it's like a super-ipad. However, it doesn't come with the pen or keyboard cover and with both (you may not need both idk what your situation is) then it comes to something ridiculous like ~£560.
You'll get people on here comparing all sorts of stuff, but I think you'll be pretty happy with the first one, I know I would be
EDIT: read through the thread and noticed your preference for 15" laptops. You can quite happily get one for this price but the issue of course is that you also want to take your laptop around with you. 13 inch laptops are better for this because they are lighter and tend to be thinner. Maybe 13" isn't ideal for gaming, but if you wanted to do serious gaming I would recommend a desktop anyway, 13" is perfect for your laptop to be a laptop and after having one, you'll think that everyone else's 15" laptops are too big.