Not quite sure to be honest. I only used three partitions, /, /boot, and swap.
The general rule is that you use twice your ram for swap space, but I've heard that this rule is no longer set in stone. Sience your using an older distro (RH8 right?) you shold probably give it the dubbled ram. So 256MB to swap.
/boot doesn't need a lot. I know off the top of my head that Fedora Core 3 wanted 100MB from me, but only used 12MB. You could probably get away with 50MB (I used RH7.2 for a month and seem to remember it asking for only 50MB), but if its no big deal to you, give it about 100MB.
I'm not 100% sure about this, but I think that whatever you dont make a partition for and specify its mount will be grouped on the / partition. So, that is probably where most of you installation files will go. The kernel will be housed here. Give this partition the ammount needed by your installation, and then however much more room you think you may need to grow (installing more programs and such).
By /user I assume you mean /usr. For this directory I found this at http://computer.laborlawtalk.com/USR
usr: User. The "/usr" directory hierarchy on Unix systems. Once
upon a time, in the early days of Unix, this area actually
held users' home directories and files. Since these tend to
expand much faster than system files, /usr would be mounted on
the biggest disk on the system. The root directory, "/" in
contrast, contains only what is needed to boot the kernel,
after which /usr and other disks could be mounted as part of
the multi-user start-up process.
/usr has been used as the "everything else" area, with many
"system" files such as compiler libraries (/usr/include,
/usr/lib), utilty programs (/usr/bin, /usr/ucb), games
(/usr/games), local additions (/usr/local), manuals
(/usr/man), temporary files and queues for various daemons
(/usr/spool). These optional extras have grown in size as
Unix has evolved and disks have dropped in price. Under later
versions of SunOS, the user files have fled /usr altogether
for a new "/home" partition and temporary files have moved
to "/var". This allows /usr to be mounted read-only with some
gain in security and performance since access times are not
updated for files on read-only file systems.
Personally, I dont know if I would give /usr its own partition, but if you would like to go ahead.
/home is your directory, so this sould be given however much space you think you need. It will store your files and your configuration files for various programs (although thoes are usually small).
I have no idea what /partion is. I have never heard of it and I don't think its standard in linux/unix systems. So the way I see it is that you will have to find the ballance of space between /home (if you want that to be its own partition) and / . Its up to you.
I also found this here http://www.bellevuelinux.org/root_directory.html
For example, directories that are installed by default in the root directory on Red Hat 9 include /bin, /boot, /dev, /etc, /home, /initrd, /lib, /lost+found, /misc, /mnt, /opt, /proc, /root, /sbin, /tmp, /usr and /var. Most of these top level directories, in turn, contain multiple directories and their subdirectories as well as files, although a few may be empty, at least initially (e.g., /lost+found, /misc and /opt).
so dont be to concerned about skipping /home or /usr if you don't want to deal with them.