Just been chatting about laptops on fbook - general agreement is for a minimum spec of 4gb RAM, 500gb harddrive, i5 2.4GHz processor (or equivalent), HDMI socket, USB3 socket, integrated graphics will do (unless you're a serious gamer.
Look for good battery life & the decision about screen size is down to weight/portability - 15.6" seems the usual compromise.
Samsung/Toshiba/Sony/Lenovo all have their fans, but "go and have a play" - not all keyboards/pads are created equal (eg I quite like my Toshiba which has 'scrabble tile' type keys - other people hate them).
Happy spending :)