Laptops will always cost more than desktops for a lower spec, and are also more likely to suffer from thermal throttling and overheating due to being rather more compact.
Given you're thinking of connecting to a 1080p external screen anyway, is there a reason for wanting a laptop rather than a tower?
I'd strongly recommend trying the OcUK forums for advise on components and spec checking for compatibility etc. Whilst it is linked to a shop, so long as you don't post links to competitor websites (e.g. PC World if we're talking about PC components) you'll be fine. They're a helpful bunch.