If laptops is a must I suggest not getting one from a "gaming brand" company. The alienware logo isn't worth the extra hundred bucks. Look up deals on Asus, Dell xps series, Lenevo, and Hp. Also I would buy an extended warranty. Heavy gaming will reduce the lifespan of your laptop's hardware due to overheating.
Wait to find something with a current gen intel I7 processor and an nvidia 560m/660m+graphics card for under $1000. Make sure to check out a bunch of reviews on potential issues the laptop might have.
Other features like SSD or standard harddrive, ram, screen resolution, and touch screen displays, etc. are up to you. I would try to get a 7200rpm harddrive but it isn't that huge of a deal if its slower. Also shoot for 8gigs of ram but with most laptops you can easily add more ram so it isn't a big issue if it has less.
Personally I wouldn't get a 1080p screen if gaming is your main goal simply because newer games would look better at 720p since your laptop won't be able to max everything at the higher resolution. You could just lower the resolution of the game but then why waste the extra money the 1080p screen will cost you. If you are going to watch a lot of movies as well though, the 1080p screen will be worth it.