What is SWAP:
Swap space in Linux is used when the amount of physical memory (RAM) is full. If the system needs more memory resources and the RAM is full, inactive pages in memory are moved to the swap space. While swap space can help machines with a small amount of RAM, it should not be considered a replacement for more RAM. Swap space is located on hard drives, which have a slower access time than physical memory.
Swap space can be a dedicated swap partition (recommended), a swap file, or a combination of swap partitions and swap files.
Swap should equal 2x physical RAM.
Provides overflow space when your memory fills up completely
Can move rarely-needed items away from your high-speed memory
Allows you to hibernate
Takes up space on your hard drive as SWAP partitions do not resize dynamically
Can increase wear and tear to your hard drive
Does not necessarily improve performance (see below)
When SWAP Partitions "Don’t Help" as in "not worthy comparing to extra storage" :
If your Harddrive has only 5400 RPM and you have little RAM lets say > 2GB.
Why ? Because the system constantly wanted to access the SWAP partition, it will eventually become very slow. Even though you now have space in the memory, everything in the SWAP partition need to be moved back over. Because the system will go slow, allot stays in the SWAP partition. This can only be fixed with a reboot. Which will take a while anyway because the system need to remove everything from the SWAP partition before shutting down.
If you would like to be able to hibernate your computer, then you should have a SWAP partition. The size of this partition should be the size of your installed memory, plus an additional 10-25% to leave room for any items that were already moved over into the SWAP partition.
If you just want a small performance boost (and you have at least a 7200rpm hard drive), then you can add a SWAP partition if you want, but it’s not needed unless you have less than 4GB of installed memory. The size of this can be whatever you’d like. However I recommend 2x the RAM as a pinpoint. IF you have enoug storage space.
If you have a 5400rpm hard drive, then you shouldn’t create a SWAP partition simply because the bottleneck will make your computer worse off. However, if you absolutely want to have SWAP, then you can still create a partition using the same sizing guidelines outlined above – but change the swappiness value to something much lower.
However in any case if you use Ubuntu as your Main OS for daily use I recommend 2x the size of the RAM. Because you don't install Ubuntu just because you have a old computer. But because you want to use the system as your Main OS.
Rather buy some extra hardware if needed instead of adjusting the system partitions to keep it running.
If you buy a game you also make sure your system is "up to date" instead of adjusting the settings to make it "Playable".
You can better have some extra space, SWAP, speed, power instead of having too short or need to resize everything later on. Because you need SWAP or space, bought RAM? Or need to buy ram fast because one memory slot or stick broke.