I´ve lived in Madrid since 2016, moving there was very difficult at first with the stampede of Eramus students arriving in September, it took me a month to find my flat as everything was going before I could view it though I chose to live alone instead of with roomies so make sure you look around well in advance.
The city is great though, already 19c today and like Spring, I live near the Retiro park just east of the centre.
I would recommend not living in Chueca/Malasaña area as it is extremely expensive for the value of money nowadays and the metro can connect you to the centre really fast from most parts of the city.
It depends where you are working and how close you want to be to the action though.
Once you get set up here it´s a very easy city to live in, lots of nightlife, always something going on and lots of nearby places worth visiting. I got my flat from idealista to and really it´s the only site worth using.
Just be aware of sites like fotocasa if you use another site, and bring winter clothes as winter here is only really December/January but it´s really cold and wet, then July/August 40c many days.
