Yes we do have two mobile phones companies, that is:
-Qtel, main countries network service, it is more expensive than Vodafone, but better network (it's what I heard, but I use Qtel). I think they might decrease the cost of the international minutes, since they're competing with Vodafone, because Vodafone is way lower in price than Qtel. And Qtel wouldn't want to loose it's "first" position.
-Vodafone, cheaper, not that good network yet not dead.

In general to first purchase a mobile card, weither it's Qtel or Vodafone, it's cheap.
As for the cost of calling to UK, for Vodafone it's cheap, for Qtel (I can't tell if it's expensive or average) because I depends on your salary. But in general, calls aren't that expensive here.

And as JF said, Skype is the best way to get in touch with your family back in the UK. Most of my friends that studies in UK, are using Skype.

About the PAYG mobile, I am not sure if it's a good idea or not, it also depends its validity. I am also not sure if it's used in Doha, I haven't met anyone using PAYG mobiles. But if you tell me how much does it cost and for how long does it last, I might tell you weither it's useful or not.

B.O.L

Loved by some, hated by many, envied by most, yet wanted by plenty!