It's different on a communal level. For plastics there ist either a yellow bin or the yellow bag which can be requested by the local Abfallwirtschaftsverband. If you have the yellow bin, just place plastics in there loosely. You could use any plastic bag then.

For paper there is typically a blue bin. All paper goes in there. Whether loosely or in any paper bag die not matter, but it has to be paper only.

Black bin "Restmüll" also loose, or any kind of bag you like to use.

Compost: typically "compostible" bags are not suited, paperbags are ideal. The compostible bags in most cases take too long to rot and have to be separated manually in the compostation facility.

So for plastic we use plastic bags and throw them away, but you can also use a trash bin and reuse it.

For paper we have a big cardboard box that we reuse until it falls apart.

For compost we have a little plastic bin.

For the black bin you can use plastic bags.

I hope that helps! I think there are no differences in other German states.

No bags in the BioMüll!

You can get gelbe Säcke most likely in your Rathaus.

Most people use trash bags, which you can buy at the supermarket, for Restmüll. But the Müllabfuhr doesn't care if the trash in the can is inside of bags or not.

You can use compostable bags for Biomüll, but most people use a plastic container which they carry to the can and empty it there. Since you can't keep compost in your house for more than one or two days a small-ish container is all you need.

Which city are you in?