Consider a hostel.

Public transport is high quality in Berlin, and sane prices.

Hitchhiking is very doable in Germany.

Booking a train ticket in advance via Deutsche Bahn can save up to 75% provided you book in advance! If you book a week in advance you still get 50% discount. A 25% discount card is also cheap, especially useful is you do further German sightseeing. But you need to order this all in advance!(!!)

I even once met some Belgian students in Berlin who used only local trains. Costed them like 35 EUR one-way, but they travelled about 12 hours from Belgium to Germany...

And, be sure to also visit Berlin centre. E.g. Alexanderplatz, Blinkenlights, CCC Berlin, and a living night time!!

PS: Don't forget to try out Club-Mate!