Recommend a laptop to fit this description?

I have had 2 laptops since my early teens; a Samsung laptop followed by a Lenovo IdeaPad netbook. Right now been finding my lenovo is slow so i mostly use my kindle fire hd or android phone now instead. My lenovo is about three years old but i just want a change. Would want a new modern laptop because (a) my kindle doesn't have screen mirroring without use of a cable (b) if i could wirelessly connect an amazon prime enabled laptop to the tv it would be excellent because prime is my only current tv provider (c) playing the sims 3 on my lenovo feels particularly slow/unreliable (d) it would allow my kindle to be a carry around novelty instead of my laptop substitute (e) a 15inch or larger laptop would be preferable to my lenovo netbook and 7 inch kindle. I hope this helps direct to a good screen mirroring laptop with a long battery and that is good for gaming (e.g. Sims 3/sims 4) and movies. My budget isn't formally worked out yet but maybe preferably kept as much below £700 as you can.

If you want a laptop that is not slow you need to buy a laptop with a fast quad core processor, and at least 4 gigabytes of RAM which is user upgradeable to more than that, You also probably need a real graphics chip, not Intel graphics, You want a real graphics chip like a GeForce or a Radeon, preferably with DEDICATED memory. Should have a 750 gigabyte drive (or larger). Typically, the cheapest models on sale at Best Buy etc. Do not meet these specs. You may occasionally be able to find a laptop to meet these specs for $399 on sale.

And note - a laptop on battery power often runs slower. A laptop that is getting hot often slows way down. Get your self a long extension cord, use yoru laptop plugged into power, anf get a good USB-powered fan pad. The pad I have had the most luck with has ONE BIG FAN