doing. Otherwise buy new… you’ll get ‘less’ but at less risk.
Your priorities should be (1) A decent fit – which you can adjust relatively cheaply if it is slightly too long with a shorter stem, some new bars (wider/narrower and more/less rise) as well as an in-line vs layback seatpost (2) A decent fork with adjustable rebound – air if you can, otherwise budget for a new soft spring if you are lighter. (3) As light as you can get… cheap bikes are often heavy – I shop with cheapo luggage scales. (4) Hydraulic disc brakes, though cable are OK (5) Last on your list is decent kit… even cheap kit is pretty good. Avoid integrated brake+gear levers if you can as it makes upgrading shifters a pain.
£500 should get you most of this – though probably not an air fork.
I’d try a Boardman or a Voodoo at Halfords or a Rockrider at Decathlon if buying new… and if you can, bring a mountain biking mate along to help. But I would definitely budget on a new saddle, and maybe a new stem and bars (a stem can be had for £15, and bars for not much more – and lots of people sell standard bars 2nd hand as ‘wider bars’ is a trend… I have 3 680s lying about).
I’ve been through an extreme version of this process sorting my 12 year old son. He’s now got a 13.5″ 2nd hand Rockhopper with a short stem and narrow flat bars (to keep the front end low), and I’ve just swapped the Dart 3 forks for some 2nd hand Rebas as he just was not heavy enough for even the lightest coil fork.