The visa is £10 - payable in English notes (none of the Scottish funny money please

).
If you were doing a sameday turnaround and use the BA self service check in machines, you could get outbound and return BP's at the same time, cutting out one hassle. Given that THY use the airport as a hub, there are international to international transfer facilities avoiding immigration (not used them myself, a colleague has).
If you want to stay overnight, the Renaissance Polat is a hotel option - about 4kn away. It's not bad in a 4* airport hotel way.