u might want to add a partition for /var like 250meg would be more then enough for a normal machine. seems like a waste of a partition but if something starts uncontrollably logging all sorts of stupid and or really important messages you wont fill up you /root partition and maybe cause a other problems or a crash.
i also like a /boot partition too i just make it like 25meg ... so i can build more than 1 kernel and its not on my / so i can umount it after i have booted ... this way a program or stupid mistake wont take out my kernel or change it without me mounting the /boot partition, then i can stupidly take out my kernel thank you very much.
i also usually make a /usr/local for programs that i install later. so id do 2gig for /usr and 5.8 for /usr/local ... but it wont really matter if you lump those together. Makeing them 2 different partitions just makes me feel safer.
as for your network connection ... just make sure you know what module you use for your nic the slack install will detect nics but if it has a problem finding yours (never seen it happen but...) ... lsmod will help you with that in mandrake. The slack install is pretty simple but you need to know what programs you want to install ... if you want a desktop machine and this is your first time id take the recommended installation. At the end of the programs installation is configuration. its pretty straight forward. The network setup is easy if you know your network settings ip dns dhcp and such.