Advice please

ChloeMM10​  You can connect almost any mouse with almost any laptop.  The one question is what kind of connector the mouse has, that is if it's not wireless.  Some very new laptops don't have USB-A ports, which is what almost all mice use.  But adapters are cheap and generally reliable; you just have to know you need one.  Or if you don't want to buy one, don't order a laptop that lacks the port the mouse needs.

For the laptop itself, this is the best I'm seeing for £500 or less, the same model on two sites:

https://www.currys.co.uk/products/hp-pavilion-plus-14ew1501sa-14-laptop-intel-core-ultra-5-512-gb-ssd-silver-10264311.html
https://www.hp.com/gb-en/shop/product.aspx?id=A2VZ8EA&opt=ABU&sel=NTB

It should be able to run all current Sims 4 packs together on high-ultra to ultra graphics settings, depending on your son's play style and how smooth he wants gameplay to be.  It also has more than enough RAM and storage for Sims 4.

If you don't like that one for whatever reason, these are all the next tier down in terms of performance, meaning high graphics settings with maybe a setting or two turned down to medium:

https://www.currys.co.uk/products/acer-aspire-3-15.6-laptop-intel-core-i5-512-gb-ssd-silver-10254475.html
https://www.currys.co.uk/products/asus-vivobook-16-x1605va-16-laptop-intel-core-i5-512-gb-ssd-silver-10265763.html
https://www.argos.co.uk/product/7665125?clickPR=plp:2:122
https://www.dell.com/en-uk/shop/laptops-2-in-1-pcs/inspiron-15-laptop/spd/inspiron-15-3530-laptop
https://www.dell.com/en-uk/shop/laptops-2-in-1-pcs/dell-15-laptop/spd/dell-dc15255-laptop
https://ao.com/product/nxk6sek00a-acer-aspire-3-a31559-laptop-silver-105399-251.aspx
https://ao.com/product/x1504vanj1617w-asus-vivobook-15-laptop-silver-104739-251.aspx

I know that's a lot of links, but since you wanted to order tonight and I don't know what other details you care about (e.g. screen size), I figured I'd provide a bunch of options and let you sort through them.  The important thing is that these should all perform roughly the same, so you can choose based on whatever criteria you want.  But if you do want to talk about the details, let me know.

This is a little faster, not in the same category as the first one but worth considering if you're not getting that one:

https://www.hp.com/gb-en/shop/product.aspx?id=A44SBEA&opt=ABU&sel=NTB

If you have more questions, about these or in general, please feel free to ask.