Hi,
You can get a 3 month visa on arrival at the Ivato Airport at Antananarivo.
It is possible to rent a house for three months and it would be the cheapest and most comfortable way to stay if you are not planning to travel around Madagascar. but if you are planning to visit other parts i would suggest that you go for budget hotels which are in plenty in Madagascar with a price range of around 40,000-60,000 AR a day (20-30 $).
I live in a rented house in Fort Dauphin and i pay 200 $ a month.
As far as monthly living cost is in concern, i think it all depends on you but if you stick to 2 beer a day on week days and another 10-12 beers for the Holy weekends and three meals a day, 2 packs of cigs a week all together will cost you around 130 $ a week (All meals at nice restaurants).
Just for your information minimum monthly wages in madagascar are 60 $ a month, so that u get an idea of how it works here.
Cheers