It depends on your use case.
If you're a very light user that only ever had one tab open in FireFox (forget about chromium) only uses two applications at a time (like Firefox and Thunderbirdand that doesn't need hibernation: No swap necessary.
medium user: With only 2GB of RAM, I would put in a 4GB swap
so you can have multiple tabs open (and individual tabs will be swapped out) and 3-6 applications open. You will also be able to use hibernation.
Heavy user: buy more RAM! ;-)
Some free tips:
I wouldn't install Ubuntu, but Xubuntu. Read here for more details.
I would take system back-ups into account. (as you will be re-installing, just go for User type 4)
/swap
size is twice the RAM (assuming you have 2 GB then it would be 4 GB). I'd just let the installer take care of it (see answer to this question). For a manual partitioning (recommended for advanced users) see: http://askubuntu.com/questions/343268/how-to-use-manual-partitioning-during-installation. – Takkat Feb 18 '15 at 08:54