Student dorm or small apartment for a foreign intern for at least 3 months

I am a 20 year old male university student studying Computer Science in Lebanon, I'm conducting an internship at a major company in München for 6 months, however I'm looking for an apartment for at least 3 months, with a possibility of extension if I found myself comfortable with it.
I love gaming and I'd appreciate a room with privacy and heating, along with WiFi connection and required rooms like kitchen and bathroom, a desk for work and washing machine. Furnished apartment with a bed is a must. I will be moving in alone around 10-13th of January depending on my visa application.
I would also need the rental agreement and landlord's confirmation of residence (Wohnungsgeberbestätigung) to register my address at the KVR, as required for my Aufenthaltstitel (residence permit).
I prefer the apartment to be close to the company I'm going to work at, northeast of central Munich, next to olympiapark. I am ready to offer documents on request.
Budget 600-800 EUR Warm rent.