How much do i need to spend 2 weeks in Türkiye,average i mean
A week to see İstanbul,Ankara, and the other week to live in a town,not a famous one,but between the mountains,and the forsts

And which would coast more,to book in a Hotel for those days,or to rent an appartment not a fantasy one ?

And would travelling on my own would coast more than to travel with an agency ?

I can tell you that I spend 250 on the flight, 250 on the hostel, and 500 on everything else.. for 2 weeks.. But we were spending way too much money! I think you can manage with about 300 euros.. (excluding the hostel and flight that is)

Depends what you want to pay! If you are from the UK, a flight to Istanbul with Turkish airlines is £200 and you can pay what you like for a hotel. I use Expedia.co.uk. But now Easy Jet fly to the other airport but dont know how much.

We took £500 and spent that easily!!!!!!!!!

Just take as much as you can afford! Buy some travellers cheques to protect your money! It depends on where you want to eat and stay!

which would coast more ?
To book in a hotel ,or to rent an apartment for the week i would be staying in each place ?

Why not have a look on the many tourist / hotel websites for Turkey, you can then get a balanced view. I personally would only stay in a hotel in a city, so that you get looked after a bit! When you say an appartment I assume you mean self catering like in a holiday resort. It is all downto personal choice in the end, as to what ever budget you have to spend.

If you leave it to last minute, xcel and travel republic do really cheap flights, especially may/sept