Compact HTPC + Civ 6 build

My dad's laptop isn't up to playing Civ 6 and he likes the idea of a compact PC so he can play it on his TV but i'm not sure how powerful the machine needs to be. He wont mind playing the game of medium settings and the HTPC will only see light use, no 4k playback or anything.

With it being in a very small living room it needs to be mini-ITX and as quiet as possible so getting a PSU and gfx card that turn their fans off until they're under load would be great. I already have an SSD he can use and i have no problem buying parts 2nd hand.

Would £300-400 get the job done?

Thanks

Anyone? Pretty Please?

This is what i could do with the budget but zero fan speed psu and gpu are gonna be a big ask.

My basket at Overclockers UK:

• 1 x Intel Core i3-6100 3.70GHz (Skylake) Socket LGA1151 Processor - Retail= £113.99
• 1 x Asus H110I Plus Intel H110 (Socket 1151) DDR4 ITX Motherboard= £64.99
• 1 x Avexir Core White Series 8GB (2x4GB) DDR4 PC4-19200C16 2400MHz Dual Channel Kit (AVD4UZ124001604G-2C= £38.99
• 1 x Cooler Master Elite 130 Mini ITX Case - Black= £41.99
• 1 x XFX XT Series 400W 80 Plus Bronze Power Supply= £30.95
• 1 x Sapphire Radeon RX 460 Dual X 2048MB GDDR5 PCI-Express Graphics Card= £104.99