It's the insurance that will set him back a big chunk of that money. A little runaround with a relatively small engine size will keep down the insurance and cars up to 10yrs old are still safe and most have security features as standard that will help.
Japanese and German cars you seldom go wrong with. Korean cars are generally very reliable and safe as well. Kia's are often for sale at second hand used dealerships but with some remaining warranty and servicing and they're cheap to run and insure as well.
I'm currently up to 250k in a VW Touraeg and before that I drove an old Nissan for two years as a mobile tack room traipsing bales, tacks, rugs, dogs and crap around every day. One of my favourite little cars was a Honda I loved driving, never had any problems with it at all but sadly it was written off in floods.
My cars get an absolute hammering as well I really don't treat them well and just rag and off road and put them through it but Japanese and German cars can take it.
Do not even get within 20ft of anything French There's a reason so many second hand sales are Renaults (Clio's more often than not) and Citroen's – they're absolute shite. Cheap to buy but that's cos they're cheap to make.
Cars with a manual gearbox or full automatics are ideal but semi-automatics, Quickshift / Tiptronic gearboxes with an automatic / electronic clutch – stay well from.
If you're not too fussed about the style, look and just what a cheap runaround, it can be worth picking up a decent second hand car at the lower end of your price range and just having Third Party no frills insurance. New drivers tend to prang, bump and scrape whilst they're getting the hang of things and it's not always worth getting full comp insurance which will cost a bit even at just TPFT.
Honda, Hyundai, Daewoo, Nissan, Toyota, Kia etc – cheap little motors and safe for new drivers overall.
Renault, Citroen, Peugeot – NOPE