Perfect Mac for University?

Okay so I'm already stressing out about going to university since it's almost the end of the school year. And as for my graduation gift, my dad is letting me choose what kind of Mac I would want to have in university. I will be taking Computer Science this fall. So I will be using my Mac for: school works (of course), heavy multiplayer gaming (Minecraft, Steam games etc.), Photoshop, YouTube and other social media. So I was thinking of getting the 13 inch Macbook Pro with Retina Display, 2.8GHz Dual-core Intel Core i7, 16 GB RAM, and 512 GB Storage. I'm limiting myself to the 13 inch one because it is lighter, smaller and easy to carry around than the 15 inch one. But if you were to prove to me that the 15 inch macbook pro is much better in my case, then I would consider choosing it.

So what do you think? Is my choice not enough, is it too much, or is it the perfect one?

Additional Question: What's the difference between i5 and i7? Is it about how fast my mac will be? What's better in my case?

Definitely go with the 13 inch one, its an ideal size. The 15 inch one may seem a little too big and heavy overall, but it has the i7 while 13 inch has i5 and bigger speakers. However, it is more expensive, so it simply not worth paying more for something that isn't as portable.

I think you are exactly right. The 13 inch with retina is my pick for the best all around laptop on earth right now. You are very lucky that you have this available to you, good luck in college.

Well, macs are really good for editing, I think Apple even gives you a subscription to some editing programs, I'm not possitive though, everything is great about this macbook but the storage isn't that good, if you are only going to do school work with it, then the storage is fine but if you are going to install a bunch of games, music, movies etc. It wouldn't be optimal, but you can always carry with you an external hard drive to save additional programs and such.

All the specs are really good for university but just keep in mind that macs aren't really for gaming, if you are just going to play games like minecraft that doesn't need a powerful GPU to run, then go on and buy it!
but games like Dying Light, Thief, Crysis 3 etc. Won't run that good because of your graphics card or because some of those games aren't compatible with apple products.

Additional Answer: If you want to compare 2 CPU's of different generations, you might want to see the models first, for example: A core i5 3570K is a lot better than a core i7 920, so I can't really tell you if a core i5 CPU is better than core i7 CPU and vice versa.