Which computer would be best for League and I?

_This is a new question based upon a previous question I asked, and the research that followed. _ Let me start by saying I don't know much about consumer electronics or computers. I am a student so most of the time my computer will be used for research and papers but in my spare time I will be playing League of Legends. (Currently and for the past three years League has been the only game I play). That being said which computer do ya'll think I should buy? I have been looking at the (MSI - GP60 Leopard 15.6" Laptop - Intel Core i5 - 8GB Memory - 750GB ) and the (Alienware X51). I must stay within a 1,000 dollar budget, of course less is more in my case. I want the computer to be able to handle having many tabs open when I have a research paper to write. I want it to run smoothly when I play LOL. Which computer would be the better investment of my time and money? Do you have any other recommendations for a computer novice such as myself? I appreciate your help! :)