Heres the deal. I don't care what anyone says, this is EXACTLY what you should do and I promise more then anything that you will not regret it and you will thank me later.
For your laptop you don't need much. Just get a MacBook Air. Spend around 1300ish on it and you'll get a pretty strong computer for school.
Then for your gaming situation and literally anything else you'd ever want to do, consider getting an older Mac Pro desktop, as they are extremely powerful and reliable, even the old old ones. I have an early 2008 Mac Pro with 8-cores, 4gb ram and it is a beauty. I run some of the most powerful software you can run such as protools, logic, final cut pro, etc. I spent $750 on the computer from ebay!!!!!! You can't beat that.
So after you get the laptop I suggest you go on eBay and get a used early 2008 Mac Pro for around $800. The graphics card that comes with it is not very good for gaming. But for under a few hundred you can get a wonderful graphics card that will meet all of your needs, thats what I did. Its very very simple to instal a new graphics card, if you don't know how you can just youtube it.
Now that you have a desktop though you'll need a screen. I highly recommend a 24' Acer. They're cheap, good size and are honestly quite nice. I am more then pleased with mine. They run at about $130 each. You could even get two because the Mac Pro has an option for two screens to be hooked up in the back.
Now with an extremely powerful desktop with dual monitors and a slick laptop that will meet all your school needs, you have only spent no more then $2300!! As you can see that puts you far under your budget. Lucky for you, the mac pro is highly upgradable. So go crazy. Put 16gb of ram into. Buy a 1TB HD. You'll still have plenty of money left over to get a customized windows computer to meet your windows needs. You could have the best of all worlds.
Hope this helps