as an advice: as you can get a Wohnberechtigungsschein (WBS), do this.
This will be an essential document for you. There are some apartments built with public funding that are available only for people with low income or who depend on state support. A WBS entitles you to apply for such an apartment. It means you do not have to compete with everyone else. Prices for such places are state regulated and lower than on the regular market. This means the Jobcenter would pay the rent for it. It is therefore absolutely central that you apply for a WBS. The WBS is issued for rooms: One room per family member, plus bathroom and kitchen. A couple with two children will get a WBS for 4 rooms, which means you cannot apply for an apartment with 5 rooms.
You can apply for such a form at the Bürgeramt, or “Public Office”; however, you need to apply at the Bürgeramt that is responsible for the district in which you are currently living. If you are living in a camp, ask members of staff in the camp which Bürgeramt is responsible for you. At the Bürgeramt, you will need a variety of documents, such as your passport, and most importantly the document saying that you are a recognized refugee with the right to stay in Germany for the next three years.
You should also pressure the Bürgeramt that your case is particularly urgent, because you have to move out of a camp. Then you will get WBS with Dringlichkeit, meaning urgency. That way, you will be treated with preference over those who have only a normal WBS (without Dringlichkeit).
Once you have your WBS, you can look for apartments that say specifically WBS benötigt, which means a WBS is required.