Don't let the 32-bit field scare you. It's going to be no worse than remembering 32 different permissions at the most.
But that's so much less fun. ;-) In practice, the lower 16-bits of the Windows access mask are used as a bit field for object-specific rights, and the next 8 bits are used for standard rights: delete, read permissions, write permissions, write owner, and synchronize are implemented. So that's 21 possible permissions, 16 of them object-specific. File system objects use 9 of the 16 object-specific bits.
Windows also supports generic read, write, and execute permissions. You can emulate UNIX-style file system permissions (and do when using Services for UNIX or POSIX APIs) by setting an object's owner and group and assigning permissions to CREATOR OWNER, CREATOR GROUP, and Everyone. With Microsoft's NFS server, you can continue to use full discretionary access control lists as well, but only the owner, group, and everyone permissions will be reflected in UNIX directory listings.
Many UNIX variants provide some form of discretionary access control lists, but most administrators are loathe to implement them, despite the flexibility they provide.