I don't know where you are based, but. Look at the map, From Biggin Hill to Barcelona is about 700 miles, from Biggin to Alicante is about 900 miles and from Biggin to Malaga is about 1000 miles. Cessna 170 cruise speed is around 110 kts, PA28 is around 140kts. Not exact math, but flying to your summer house 5+ hours renders it useless pretty quickly. To have reasonable costs you need at least Citation Mustang/CJ1 or similar.. but. although it can be done as a fresh PPL , I cant reccomend to do it. If I would be in your shoes, I would go for a PPL course in US doing FAA licence. Then hour-building to at least 500 hours in single engines and then most reasonable choice would be doing a ME and IFR rating and only then buying a KingAir 90/100 or entry-level single pilot jet and keeping it in N registry with your FAA licence.