A car bought in Turkey will cost you about 180% of what you would pay for the same car in the UK. The only economical car to run is one powered with gas, not petrol. A gas tank in the boot.
It is correct that if you bring a car from outside, you must take it out of Turkey every 3 months, and in theory, wait 3 more months before bringing it back in.
We are residents, we do own a car bought in Turkey. It has MA plates, signifying a foreign owner. This kind of car can be kept as long as your residence permit is valid and not a day longer. And you must have a semi-annual or annual inspection depending on the car type.
You might consider leasing a small car or negotiating a long-term rental. I know a couple who have this arrangement with Adda Tours. They get their car when they come, keep if for several months, give it back when they leave.