Please could somebody help me with my slax installation.

I'm using a HP Compaq nc 6000 with a completely erased (reformatted) hard disk. I want to install slax on the hard drive. That's very well documented, but there is no place to copy /slax to. So I think I would have to partition my hard disk and then to format the partitions. I've absolutely no experience as admin.

So how many partitions of what size should I choose?
What filesystem would be better FAT32 or ext4?
And what are the right commands for that purpose?

Thank you!

Keep it simple and just create one partition for the OS and a swap of 2-4GB, depends upon RAM that you have.
If you are going to install a Linux system, you should use a Linux filesystem and not a windows filesystem such as FAT32.
What operating system do you have to work with? Any Linux OS on the drive or on a Live CD/usb should have the software needed. You can download and burn a copy of GParted to a CD to use. It is a graphical and well documented partition manager.

https://gparted.org/download.php

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At the moment I have a slax live cd, a not yet bootable usb stick with slax on it and nothing at all on my hard drive.

the slax doc says that FAT32 or ext4 would be appropriate filesystems and they want to have msdos style partitions.

Being not experienced, I'd still suggest you partition it with a split root and home that way your home data is safer than it would be if put all onto root / partition. As far as swap goes, I'd put it at the end.

root /
/home
/swap

Because you might find you do not need a swap then it can be easily regained and merged into the home partition.