Pay anyone in advance. Never use WesternUnion, Moneybookers, Paypal or cheques to pay anything related to rent before you come to Hamburg.
WesternUnion and Moneybookers is completely uncommon in Germany and never (close to 0%) used in Germany.
What to avoid when coming to a WG or apartment:
It is common that Students share appartments - this can be in a privately rented appartment or in a student dorm.
It is not part of the culture to share rooms, so you will stay in your own room and share the bathroom/kitchen with the others. If you want to bring your collegue, girlfriend or other to live with you for the semester or a prolonged period of time your flatmates will probably not like it.
What Students living in the dorm or WGs like:
Usually people will want to meet you before you can move in. - They have to put up with you, right? (So it can be easier to get temproary housing and then meet people.)
How much should I pay?
Rent typically consitsts of these parts:
Rent (Kaltmiete): In Hamburg: 5€-9€ per squaremeter
Costs for facilities: 3-5€ per squaremeter
Costs for heating: 0-2€ per squaremeter- usally goes together with costs for facilities, but can be extra
Costs for Internet - usually extra (ask)
Costs for electrical power - usally extra (ask)
Should be maxium 3times Rent(Kaltmiete) - everythingelse is scam
Where should I live?
If you find something: Take it!
Don't be too picky about it. The room situation is terrible in Hamburg
But if it's really far out? As a student you get a ticket which is valid for the whole public transport system, check here how long it takes you to uni: http://hvv.de
But what if its just for a couple of month? Take it. You can get another place for a couple of month later.
What if I run into problems?
Two things to keep in mind:
Actually read what is in your contract.
You can ask for help at the AStA of TUHH - they can also get you free legal advice if necessary.