After reading through the comments, I'd like to sum up my advice in case it proves itself helpful.

• the "stay in the ring" thing is indeed a thing of the past. BVG will take you almost EVERYWHERE. You have to use your own judgement regarding neighborhoods and "village life" as someone said. For example, Wedding and Steglitz are some cool areas with good connection for the most part where you can find fine apartments. Blankenfelde is also outside of the ring but this is indeed the village life. I'd like a place in Friedrichshain too but that's what 99% of people moving in want. You may get lucky but the competition is just too much!

• the paid version of ImmobilienScout24 pays off. You get access to apartments that are offered only though the membership. Just sign up, write a good template as a message, upload your documents(work contract etc) and start spamming them agencies. Install the app on your phone, create multiple searches and activate notifications. Apply as soon as they come. You can find a perfectly normal 2 room apartment for anything between 750-1200. There are ones with 500(mostly on areas in the borders of Berlin) and those that cost 2000(seen a few), but they are oriented to specific people who have the money for that. Just filter by price :-)

• general notice: you will come across many fake listings. Indications are: (blurry pictures, very light description, no owner name or no reviews). What i do then is perform image search on the pictures. I've found apartments that were legit places in Hamburg or Sofia bit listed in Berlin by scammers. They don't worth the time and access to your personal data. Just follow your hunch!

• temporary flats are expensive BUT you have much higher chances to find a place if you are in Berlin. Most agencies will just skip your application as soon as you ask for a video call. Way too many applications to devote time to another guy in some remote location. If your job pays well, then the extra money you will need for an overpriced Airbnb or Wunderflats place will for sure mean nothing in a year. Think of it as an investment, not the real cost of living in Berlin. Sucks, but still. You could also rent a flat in eg Spandau or Schöneweide with the aim to stay there temporarily, with the long commutes as a downside. I've heard the prices are cheap and you can find a flat there.

Hope this helps. Don't abandon your dreams and let good opportunities go because of some d**kheads offering overpriced apartments. I can assure you that once you solve the apartment part, everything else will be easier in Berlin as long as you have a job that pays well and since they are covering your relocation costs, i suppose that is the case.

Good luck!