awesome sticky.
some notes perhaps worth mentioning:
Last time I bought a bahncard they where able to take my picture there with a small digicam, very surprised by that. (It is ugly but at least I did not need to ruin a photo for that) The photo needs to be the size of a pass port, but you can cut that yourself.
Second it may be worth mentioning that you get a temporary bahncard right away - so if you want one because it is cheaper, they will be able to give you a paper version right away. I am not sure how buying one as a foreigner works.
This will roughly take you 15-30 minutes of filling that one out.
Note on the city tickets: this *only* applies when you have a ticket for >than a certain distance, I think it is either 60 or 100km, so just by buying any ticket does not give you a public transport ticket as you suggested.
Verkehrsbünde also sometimes will make you incapable to buy a ticket online, you then need to find out if there is a close alternative to enter. In my case: Lübeck is in one of those Verkehrsbünde, so I cannot buy Lübeck-Hamburg online. But I can buy a small city next to Lübeck to Hamburg online, because that would be three states and therefor is considered normal train travel.
hth