Regarding the tourist visa, if you go to the Al Maha desk at Arrivals and pay, they sort the visa and meet your guest from the plane, reunite them with their luggage and clear them through immigration and deliver them to you. They need 24 hours notice, the passengers full name and nationality and the flight no. It is invaluable and has worked many, many times for my family. My mum loves being met at the steps of the plane and being whisked away.
You can use BA if you want but remember to check Etihad and Gulf Air as well. It is sometimes cheaper to book a BMI flight as it is still Qatar Airways but they are trying to promote it at the moment. My friend saved 200 pounds and went on the same flight she would have done if booked QA.
Regarding where to stay, that's up to you. I'm sure you will get lots of advice about that.
All the best, JJ