Am guilty of doing the same thing as your family!
Just relocated my parents to the Costa del Sol after 4 years of nagging! 😀 They rented first (my recommendation) whilst taking their time to look. We looked at over 30 properties together (private and agency) and they finally settled for Calahonda as offering the best value for money/size/build quality combination.
It is still possible to get a decent apartment in this location for around 150.000euros – e.g. some of the urbanisations from the mid 80’s are well looked after, have low community debts and may come fully furnished. Many of the big boy agents here would prefer to sell you something off-plan as they will get paid a nice fat commission on exchange rather than completion. Me, I prefer big old re-sale apartments that need a bit of tlc, possibly a new kitchen and a re-paint. Banks here like these type of apartments too and seem to give generous mortgages.
To comment on your Ruskie Godfather question 😈 – Yes, there was bad press re:influx of Russian/E.Europe mafia money but properties purchased/lived in by these people mostly in the Alcaidesa region + Sierra Blanca (well posh) and most of the naughty boys are now jailed or bailed (incl. lawyers, mayors, etc.). The matter is being sorted out and you’re probably not likely to run into the characters involved on a daily basis.
To comment on your illegal build issue: get a good lawyer (they can verify within 24 hours if a property is legal), don’t buy too far inland (where most of the problems are) and if something seems too cheap/good to be true then it probably is (you don’t sound like you fall into the daft Brit category).
Happy hunting on the Costa and the Côte!
p.s. the lingo isn’t too hard to pick up either if you already speak reasonable french.