There are different concepts about this. Absolute minimum, you need /root and /swap. Some writers recommend making different partitions for the standard user areas, such as /var, /home. The advantage is that you can then re-do the /root partition without redoing the others. Whatever I "guess" as the right size for my linux /root, I always guess wrong and run out of space, so I like to give it everything but the swap space. Swap should be roughly 2x your ram unless you have more than 512megs. I have 256megs., 512megs swap, but it doesn't really seem to get used very much -- when I check, the swap is usually empty.
There are several file systems and I am no expert. This is what I seem to have found out: EXT2 is obsolete unless you have something requires specifically EXT2. EXT3 and ReiserFS have replaced EXT2 (and there some other ones as well.) EXT3 and ReiserFS are "journaling" systems that allegedly avoid the need to "scandisk" and "defragment" that you end up with on a VFAT (Windows) partition. "Journaling" sort of caches disk transactions and cleans them up in the background. Some people have nevertheless reported "fragmentation" issues under journaling systems, but so far it ReiserFS is working fine for me.
If you are installing to an existing Windows harddisk, there may be some problems. I did one install (partitioned by the Mandrake partitioner) and when I ran Windows defrag it killed the Linux partition. I then used Partition Magic to make partitions before installing Linux -- I made EXT2 and swap partitions with Partition Magic and then changed EXT2 at install time. Seems to be working -- anyway, has survived "thorough scan" and "defrag" on the Windows partition.