[Effendi]

Aldi is surely the best choice. Anyway, avoid the prepaid starting kits since I think they are all sim-locked phones, and surely not cheaper than sim-free phones you can get on eBay. The problem with eBay is that you don't have much time, but you can also buy a phone on eBay.de and then take it directly in Berlin (there are many sellers from the German capital).

Vodafone has no sense at all, unless you plan to visit other countries where they have their network, but if you plan to visit many countries there are other better solutions, IMHO.

I really think it's not a problem to get an Aldi card, or maybe a Tchibo (more expensive, but Tchibo stores are usually in the center of every German city, so very easy to find).