If you don't have a problem with ID registration in a shop, you can get a one month free test Sim with unlimited Internet data and unlimited calls/SMS (inside Germany with German numbers) that doesn't renew itself at shops from o2 or online.
https://www.o2online.de/e-shop/tarif/netz/o2-testkarte
That should be the best solution in terms of price (no cost at all) and data availability.
O2 is working fine in cities, on the countryside it is sometimes not so good, but that can happen with all providers.
T-Mobile is the worst indoors, but works fine outside in most Places.
Vodafone is in the middle of both, when it works, it's good.