Minor issue, 'cause you get there eventually, but use http://reiseauskunft.bahn.de/bin/query.exe/en from the start, not bahn.de
"Why not first ask the date of travel and then where to where, and then bring up a timetable to choose from?". There can easily be 20-30 connection during that "date of travel" (24 hours). This narrows it down a little.
You know the day you want to travel, and the time you want to leave (or arrive), and where you want to travel between. That's what they ask.
I don't know if it will help any, but take a look at the section on my website for using the Bahn website.