I get the idea that you thhink that permission have anything to do with the mounting. This is not the case. File/directory ownership (user.group) and permissions work through your complete directory. tree from / on.
When you have a permission problem with a file/directory then please SHOW us what they are. Specialy as you say you changed there things and you do not show what they are now, most other people will have no idea.
If I understand you correct, you want to allow all users to be able to create and remove file in /media. Then you should of course see that the options allow that. Thus when root:root is the owner, the permissions should be rwxrwxrwx to allow user root, all users that are part of group root and all others to read, write and acces the indodes of /media.
But take care. This means that when user aap cretes a file there, user noot is able to remove it. I do not know if that is what you want.
An alternative is to make it the same as /tmp:
henk@boven:~> ls -ld /tmp
drwxrwxrwt 17 root root 12288 16 mei 21:30 /tmp
henk@boven:~>
which uses the “restrivted deleteion flag”. You see the t at the end of the permission string. The description in man chmod says it all"
RESTRICTED DELETION FLAG OR STICKY BIT
The restricted deletion flag or sticky bit is a single bit, whose interpretation depends on the file type. For directories, it prevents unprivileged users from removing or renaming a file in the directory unless they own the file or the directory; this is called the restricted deletion flag for the directory, and is commonly found on world-writable directories like /tmp.
In other words, user noot above can not delete something that is owned by users aap.
I hope you are also aware of the fact that users that create directories/files thjere can protect them from other users by setting the permissions of those files owned by them.
I have no idea if this fits your “I want it to be mounted for any user to have write access.” (where the word mount for anyuser is incorrect, one does not mount “for a user”, one does mount a file system on a mount point and the permissions are what they are).