Need help with buying/building a gaming computer

Solution
gaming laptop is never a good idea, too small space for heat dissipation, so overheating is kind of normal.
BYO is the best choice:

PCPartPicker part list / Price breakdown by merchant

CPU: AMD - Ryzen 5 2600 3.4GHz 6-Core Processor (£149.99 @ Amazon UK)
Motherboard: Asus - PRIME B450M-A/CSM Micro ATX AM4 Motherboard (£62.86 @ Amazon UK)
Memory: Patriot - Viper 4 16GB (2 x 8GB) DDR4-3000 Memory (£137.20 @ Amazon UK)
Storage: Crucial - MX500 250GB 2.5" Solid State Drive (£53.97 @ Amazon UK)
Storage: Western Digital - Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£34.74 @ Aria PC)
Video Card: Zotac - GeForce GTX 1070 8GB Mini...
gaming laptop is never a good idea, too small space for heat dissipation, so overheating is kind of normal.
BYO is the best choice:

PCPartPicker part list / Price breakdown by merchant

CPU: AMD - Ryzen 5 2600 3.4GHz 6-Core Processor (£149.99 @ Amazon UK)
Motherboard: Asus - PRIME B450M-A/CSM Micro ATX AM4 Motherboard (£62.86 @ Amazon UK)
Memory: Patriot - Viper 4 16GB (2 x 8GB) DDR4-3000 Memory (£137.20 @ Amazon UK)
Storage: Crucial - MX500 250GB 2.5" Solid State Drive (£53.97 @ Amazon UK)
Storage: Western Digital - Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£34.74 @ Aria PC)
Video Card: Zotac - GeForce GTX 1070 8GB Mini Video Card (£359.99 @ Novatech)
Case: Phanteks - Enthoo Pro M ATX Mid Tower Case (£59.86 @ CCL Computers)
Power Supply: Corsair - TXM Gold 550W 80+ Gold Certified Semi-Modular ATX Power Supply (£67.99 @ Amazon UK)
Total: £926.60
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-08-30 21:51 BST+0100
 
Solution
For 1080p/60hz, something like this should be pretty good...

PCPartPicker part list / Price breakdown by merchant

CPU: Intel - Core i5-8500 3GHz 6-Core Processor (£178.47 @ PC World Business)
Motherboard: MSI - B360M PRO-VDH Micro ATX LGA1151 Motherboard (£65.99 @ Amazon UK)
Memory: Team - Vulcan 8GB (2 x 4GB) DDR4-2400 Memory (£68.99 @ Overclockers.co.uk)
Storage: Crucial - MX500 250GB 2.5" Solid State Drive (£53.97 @ Amazon UK)
Storage: Seagate - Barracuda 2TB 3.5" 7200RPM Internal Hard Drive (£51.59 @ Aria PC)
Video Card: MSI - GeForce GTX 1070 Ti 8GB DUKE Video Card (£360.87 @ Amazon UK)
Case: Corsair - Carbide Series 88R MicroATX Mid Tower Case (£40.55 @ Aria PC)
Power Supply: Corsair - TXM Gold 550W 80+ Gold Certified Semi-Modular ATX Power Supply (£67.99 @ Amazon UK)
Total: £888.42
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-08-30 21:53 BST+0100