Compound ! unless you are willing to pay extra to live in a villa. Villas are not cheap here in Qatar ! I moved like a month ago and been asking myself the same question, but i decided to go with the compound. But again, i dont have children.
You can still find some really REALLY cheap villas in Al Wakra - like 25 minutes away from the city center. A friend of mine lives in a nice stand alone villa and she pays like Q.R 15,000 a month + utilities. Now in Doha, you can find a two bedroom apt , semi furnished for 6000 or 7000 ( my compound for instance ) and its close to the courniche and Suoq Waqef. Compounds usually have gym, swimming pools, sauna and jacuzzi !
If you are looking for a villa here in Doha, you'll be talking about 25,000 to 60,000 QR a month !

Wish you the best .