Need advice on cheap but powerful laptop

I need a new laptop but there's so many i dont know where to start, my current laptop is a samsung at 2.2ghz but it has an intel graphics card and now has charging problems.

all my life i've had an intel graphics card and i've had no end of problems so definitely want to avoid this. what other graphics cards should i be looking at?(preferably one that comes with the laptop? but isnt integrated)

i will be using it for all kinds of things and would like to it be powerful enough to handle multiple youtube tabs open at the same time etc along with a video/music on vlc player on at the same time.

A big requirement to do with the graphics card is it must be modifiable to play old games such as heroes of might and magic 3 and star wars knights of the old republic 2(i know it isnt easy to get this game running but i know it's impossible with integrated intel) and i would also like it to be capable of playing at least the current games(something like ark: evolution) on hopefully a medium setting(high settings would be great, but im more than happy to compromise on quality of new games for them running smoothly without lag and a cheaper price)

would like a half decent size keyboard and the weight of it isnt really a problem as long as its not ridiculous. considering my previous laptop is 2.2ghz and it seemed to work ok, something around this or a bit higher should be ok.

i will most certainly buy the laptop second hand, and most likely off ebay so please take into account second hand prices. My budget is £250 at absolute, £200 would be ideal. I'd also like to stay away from windows 10, windows 8has been doing fine.

Thanks in advance!