I believe that you can get a resident's visa for as little as 3 months, which seems pointless when you can use a visitor's visa for 90 days. More usually, people take them out for 1 or 2 years
Here's a copy of an email that I sent to friends around a year ago, which should give you an idea. It was sent to people who were UK state pensioners, so they didn't need health insurance, but that would be an additional charge, if you're under that age
Before you go to Mustafa, please make sure that you each have 4 x passport photos & a printed copy of your e-visas + a notorised translation of each of your passports.
Here's an outline of costs:
Mustafa: 150 TL / per hour - allow a couple of hours, as he has to make 2 x application for the DGMM & check 2 x lots of paperwork
Photos: 2 x 30 TL
Tax: 2 x approx 560 TL (that was for 1 year so possibly close to double for the max 2 years)
Passport translations: Last time I was there with anyone for this is was 200 TL a pop, but that was a number of years ago, so probably 300 + now
Tapu certificate : 11.50 TL - not sure if 1 will suffice for the both of you or whether you need 1 each. This was for a home owner, so not sure how it works with a tenant
Hope that helps a little