Well... I think setting a rough budget and an idea of what kind of games you (or the kids) want to play would be a good start. And then blow the budget anyway  :-$

Let's have a budget of £300 upwards for the pc, any new monitors etc can be extra.

Core i5 minimum, 8GB tbh, 1TB hdd

This looks like a decent chassis, no?

https://www.ebay.co.uk/itm/252847552063

That reminds me of something from a film or a game. Maybe HL2?

I got a custom one built from Scan for my BIL the year before last and was very impressed with the price and service.

Depends what you want it for. Mainly, no gaming, a bit of gaming, or hardcore gaming?

Personally I'd take a look at some of the charts and guides on Tom's Hardware. It's surprising how capable budget graphics cards can be these days if you're not trying to push them to 4k resolutions or run the latest games with all the fancy graphics turned up to max. Avoid choosing a specific brand, as although Nvidia currently rule the high end of the market, AMD do make some compelling cards a bit further down. It all depends on your budget level.

Lastly, you could also consider a refurb PC. CPUs have really stagnated over the last few years performance wise. My primary PC is still using a Core i5 from 2009 and a graphics card from 2013, yet will play Deus Ex: Mankind Divided at 1920x1200 whilst still looking pretty good (not on maximum quality obviously).

To be honest, I think you're looking at more like £800 for a new PC with that kind of specs. Yeah, I know...
I'd be aiming for a Ryzen 5 1400, 2x 4GB DDR4, AMD RX470 GPU, etc; that should see you through for a fair few years, even better if you can get an SSD as well since they make everything seem so much more responsive.

Really? My laptop (i5, 8gbtbh, 1tb, GT750M 2gbtbh) was 700ish a few years ago.