Looks like the partitions size is a bit messy, it would be better to reinstall the system.(backup your data)
Lets talk about how to partition it:
Simple way just 2 partitions: the main or root partition which is the / and swap, that is the most basic setup.
A bit better setup would be 3 partitions with: / , swap and /home.
Now to have a more controllable setup, 4 partitions: /boot , / , swap and /home
There are more complex setups but for a desktop use the ones here will do the job.
Now about the sizes, keep in mind one thing, the distribution that you are using may use more or less space than a other distros, and the size of the disk, you have to figure out how much your distro uses.
It will be about
200-300mb for /boot
1Gb-30Gb(depends on distro) for /
at least same amout of RAM or more for swap
and the rest of the available space for /home
It is just an idea about how to setup the partitions it may be different in other scenarios.
About the partition types if you have an old machine with more than 8 years old it would be better to use ext3 or even ext2 if the processor power is low, it will speed up the whole thing(there other types of partitions some people like a lot XFS), now for machines about 5-7 years old most of them use sata drives, ext3 or ext4 or XFS, is what most people use for their desktops.
Here some info about partitions(this is a bit old but gives a good idea about file systems):
This one about partitioning(old doc but give a good notion):