Is this the best bet for Minecraft?

Hi and thanks for reading this! I really know very little about Minecraft, but my 8year old daughter loves it and plays on her ipad mini. For her birthday next month she wants a laptop so she can play on that instead. She has seen the game on other laptops, like her cousin's Mac.

Ideal budget is $500-$800. (Would really like to keep it under $700...) Windows 8. Screen size 13-16". What do I need to look at next? Processor speed and type? Ram gb? Dedicated video card? I would like to consider used and refurbished in order to get more bang for buck, but only from a seller that offers warranty/support.

I really want to avoid getting my daughter a laptop for hundreds of dollars and then seeing her disappointment or frustration because it is not powerful enough to do the things in Minecraft that she expects to be able to do. She wants to start playing on my PC, but I'm afraid my recently updated PC will offer resources/power/speed that she won't get in a laptop in our budget range, and then she won't like playing on the laptop!

I found this one from HP (specs below). I think it is the best one in the $800 range because it has an 850 series video card as opposed to so many other configs that have the 840 card... And it has other things I want like backlit keyboard and dvd drive. But I'd love to find a Win 8 with touchscreen, DVD drive, backlit keyboard, for around the same price (and of course with the right processor and video card for Minecraft). Not sue that is possible though...

$880 (might be additional discount on price)
HP ENVY - 15t Windows 7 Laptop
L8C63AV_1
Windows 7 Professional 64
5th generation Intel(R) Core(TM) i7-5500U Dual Core Processor + NVIDIA GeForce GTX 850M 4GB Discrete Graphics
15.6-inch diagonal Full HD WLED-backlit Display (1920x1080)
8GB DDR3L System Memory (1 Dimm)
1TB 5400 rpm Hard Drive
Backlit Keyboard with Fingerprint Reader
4-cell 48WHr Lithium-ion Battery
SuperMulti DVD burner