For non-percussion playing composers writing out percussion parts can be quite a challenge, partly because they don’t know exactly how to notate the parts. These key maps for drum set and some other common percussion instruments can help.
Here is a short article on how to write out drum set parts for big bands. With most “groove-based” percussion playing (jazz, latin, rock, etc.) it’s not necessary to write out the complete percussion part for the player, since what they will come up with to play is usually hipper than what you can notate. On the other hand, a lot of big band drum set parts don’t have enough info for the drummer for easy sight reading. There’s a balance that you have to strike to give you percussionists or drum set players enough info to work from to blend and balance with the band (dynamics, phrasings, hits, etc.) without cluttering it up too much.
When in doubt about how to write something, get in person with someone who plays that instrument and get their help.