Here in Berlin The Material List was sent out along with the official confirmation of the school place, but I think some schools don't do that until the first week of school or the day of the Einschulung.
The stationery booklets usually have numbers on the front, so you'll be told 3x no. 27, 6x no.10 etc. We also had to buy a specific number of plastic coloured folders to go round the booklets - a different colour for each subject. If you already have The List when Aldi do their annual school materials week, all well and good, because the Aldi stuff is inevitably good value. The problem is if you don't have The List, there's too much risk that you'll buy the wrong things and then they're wasted.
It is imperative that you buy the largest size of Schultüte for the child being eingeschult. The smaller Schultüten are only for siblings or intended as 'supplemental' Schultüten from grandparents etc. In Berlin the Einschulung (at a Grundschule) is always on a Saturday, so there's a ceremony and the kids then troop off to do a 45-min lesson when they learn a song, which they then perform to the proud parents, then everyone goes home and they get to open the Schultüte which they had been carrying around since the morning. The whole thing is finished by 1pm, so people go off and have a meal out or a family celebration. It's A Very Big Thing.
Don't forget to label everything - yes, every single bloody pencil. And they'll still get lost by the Herbstferien!
Once the kids get a bit bigger (9 or 10) you can give them 40 euros and send them off to do the materials shopping themselves a week before term starts.
In Berlin you have to buy the textbooks too - there's a strict upper limit of 100 euros per child per year, with exemptions for lower-income families.
"I'm surprised you don't know the class allocation yet" I think every school gets to choose how this is handled, but both at junior and senior school (in Berlin) we didn't find out the class allocation or teacher until the Einschulung. All the names were read out, the kids went up on stage, and then the entire class marched out together.