Can I do a fresh install of Ubuntu 13.10 on my VAIO laptop?
YES, you can buy a SSD or a normal hard drive what ever you like put it in your laptop and run Ubuntu on it and your laptop should work just fine.
In fact, chances are that you will not have to look to much for the drivers since Ubuntu has a lot of them in its repository and it should be a easy transition.
If for any reason you will not like Ubuntu you can decide to buy a Windows license later anyhow.
Since all the Ubuntu drivers you need are likely to be Ubuntu repository, you don't need anything from Sony. As far as I know Sony will provide Windows drivers only and those are useless in Ubuntu.
Create a LiveDVD/USB of Ubuntu and
Try without installing. This will tell you that everything works or not.
If everything works, go ahead with the SSD and install Ubuntu.
Hope this helps