You'd likely need a decent NVR with 4 x POE channels - NVR's don't come with hard drives as standard, so you'd need to factor one of those in as well - and to use a surveillance drive rather than a normal hard drive.
My own experience is with Hikvision - others might have further recommendations of other brands.
No brand is 'perfect' unless you're spending serious money, but Hikvision tends to give decent £ for £ value, decent reliability, decent performance with the odd glitch, but nothing that can't be overcome.
You've linked to a Hilook system - that's the budget brand from Hikvision - and will be better than the Amazon links you were originally looking at, but may not have all the features you'd find on a full-blown Hikvision system. The Amazon products you've been looking at are like a 20 year old Lada or Skoda, the Hi-look products are like a 6 year old Ford Fiesta, the Hikvision products I've listed are more like a recent BMW 3 series, but there are of course plenty of camera systems that are between Audi Q7's and R8's. On a forum like this you won't get any recommendations for the Lada or the Skoda - not many would go for the Ford Fiesta - most would plump for a 3 series BMW or above. But at the end of the day - a camera system is a camera system - you pay your money - you take your choice
This would be more likely along the lines of my own recommendations based on what you've stated you wanted - comes to about £550 excluding VAT - with the basic tools needed for building your cables. The cable of course needs to be external grade if it's going to pass through a wall or window and be exposed to the elements. I've spec'd a 1tb drive. You might need additional brackets for the cameras depending on where you're mounting them and to what. These are typically £15-20 a piece.
Various suppliers are out there - but not all will directly supply an end user - so you might not be able to find the exact prices you see here:
You'll also find that if you're buying direct from a wholesaler - you won't necessarily get the same support you would as a consumer buying something from Currys. If you can't work out how to make it work, although most suppliers will help with fault finding - they won't baby walk you through a full install. From what you've said, you're confident with IT, networks and cables - so you should be in a better position than most in terms of people that want to fit their own system. Good luck with whatever you choose.