Cheap prepaid Internet for short stay in Germany? [merged]

[inquisitor]

Regarding internet access O2 loop and Tchibo are the same service (both use the O2 network), however Tchibo is € 5 cheaper per month. But if you already have some of those free O2 Loop SIMs waiting for you, it doesn't really pay off to buy a Tchibo SIM (and pay shipping costs) for a single month of use.
Regarding connection software the T-Mobile Web'n'Walk Compact card II, which is produced by Option, should work with this version of O2's "connection manager".
But if you use O2 Loop, you could also use the T-Mobile connection software, since O2 Loop doesn't require a (correct) APN to be set. So even if T-Mobile's APN is preconfigured in the T-Mobile software it will still connect through O2 Loop.