Help in finding the right laptop?

I've been looking for a good laptop to buy for quite a while now but cant seem to find one that fits perfectly.

I'm looking for a laptop that can suit my student needs as a college freshman, but at the same time it should also be able to handle some casual gaming, have a clean design and generate pages quickly. Games wise it should handle League of Legends at medium settings and Minecraft with no lag.

I don't care about the battery life, and can overlook things like no keyboard backlight or a shitty touch pad. It would be a plus if the screen was touch though.

My budget is around the ~$1000 US dollar range. I've already looked into a few laptops, the Dell XPS 13 and ASUS ROG series being among them but they were too expensive.

Desired Specs

Processor: At least an Intel i5, but i7 preferred. But if the difference between the two is a huge price difference in exchange for a small performance drop, then I'm fine with the i5.

RAM: At least 8GB, but up to 6GB is fine. The more the better.

Hard Drive: 256GB SSD minimum. Less would be okay depending on the laptop.

Screen size: 13"

Weight: Under 3lbs. A little over is fine.

I've found one laptop that was absolutely perfect for all my needs, the ASUS UX305. However one of things that is making me reconsider is the Intel Core M processor because I'm not sure if it can handle the games I want to play. I've looked in several sites but they've all given me mixed answers.

It would be preferred if I could buy it on Amazon. Thank you!