Islamabad is one of the safest cities in Pakistan. Crime rate is very low. Rent varies as per size of the residence (1000$ to 10,000$ and above) in sectors like F-6, F-7, E-7, E-9. Most of the foreign security agencies like black water etc has rented houses in these localities, so the frequent checking is normal routine here. The most suitable sector for residence may F-11, F-10, F-10, G-10. Then there are sectors like F-8, G-8, G-8, I-9, I-10 where the rents are almost 200$ to 800$ depending upon location and size of the residence. Normally, the dealers ask for 3-month advance rent as security deposit. The monthly expenses start at least from 800$ to your pocket's strength and life style.
If you like to live in the suburban areas then Bahria Town is the best choice where U can have a two canal villa portion just for 500$ to 800$. It is very secure and state of the art place for living with all the facilities. If go for PWD, Police, Foundation, Sawaan Garden almost 20 Kilometers from main city, but now a part of the city on Lahore bound Highway, then U can have 50ft x 90ft villa just for 250$ to 500$. This place is adjacent to Bahria Town and equally safe and have all medical facilities and the necessities of life.