I have just starting Ubuntu as my primary OS and everytime I have to install something I generally try to find .deb files as that seems convenient, but someone on another forum told me I should always use tarball files.
So can you tell me what would be the ideal recommendation and why?
But on a personal note:
Using .deb lets you keep track of the install. (e.g. So you can uninstall or upgrade later). Installing from source (.tar.gz or otherwise) puts you in charge of what and where to install. You can have multiple versions installed at various locations, and they are hard for me to uninstall. Personally I prefer to .deb files.
You should not normally find and randomly install any Debian package from the Internet. Use apt-get to add/remove packages and apt-cache for querying.
Always look for software packages in official repositories. They are well tested for stability and performance. Installing packages using .deb files is advisable, as it'll take care of dependencies and as answered above solves a lot of maintenance issues. If you want to install using tarballs, then make sure that package dependencies are met.
I use deb files much more often than tarball files mainly because installing the item is much more simple with deb files than having to compile and other steps for tarball. I don't think there is any difference between the two as to what they give you, you just receive it in a different way.