I'd +1 the desktop idea unless you really need the portability of a laptop. They're easily serviceable, you can put it together with exactly what you want, and upgrading later is often really cheap with second hand parts. They're also easily cleaned - laptops much less so, especially if you're going to be running games on it (more load = higher fan speed = more airflow = more dust buildup.)
My decade old desktop is still going strong as a media PC after whacking an SSD and second hand upgraded CPU in it - that's the only upgrade it's had from new; cost me just north of ÂŁ60 for both parts (and it was a budget machine when it was put together!)
"Gaming laptops" (basically meaning they have dedicated graphics) will also usually blow your ÂŁ500 budget out the water.
That said, whatever machine you're after (laptop or desktop):
- Don't accept anything less than an SSD these days, ignore "HDD" or "hybrid" drives off the bat - and I'd be looking at a 256GB drive;
- Preferably 8GB RAM, minimum 4GB;
- Look out for an optical drive if you still need it - many machines these days come without;
- CPU spec is generally less important than people tend to think these days, but with a budget of ÂŁ500 I'd be shooting for an i5.
- If battery life is important to you, check it before buying (many forget this bit!)
Ebuyer is a good place to look generally for these things - they're often among, if not the cheapest and I've never had any issues with them.
Quickly pulling one out that's around your budget and meets the above specs:
Lenovo V130 Laptop - Laptops at ebuyer - https://www.ebuyer.com/874325-lenovo-v130-laptop-81hn00nguk