Where did you get Thunderbird from ? It's available in the Ubuntu
Software Centre ( under 'Applications' ) and generally that's the
first place to look for software - there's a simple 'Install' button
to make the process quick and painless

Once installed, Thunderbird appears in [ Applications / Internet ] and
the icon can be dragged up to the top bar to create a quick launch.

Note that the programs in the USC may not be the very latest ones but
have been checked that they won't break other programs. Installing
manually from other sources has the potential to break things if you
aren't careful - not that Thunderbird *should* do that, but worthwhile
being aware of as a new user :-)

There's always a trade-off between being cutting edge and stability in
any OS, not just Ubuntu, and is partly why the USC exists !

Generally I don't think of the Software Center as the first place to look
for software for the system. I usually use Synaptic Package Manager,
at least for the big items like Thunderbird.
But that may just be me, for little things I have looked in Sofeware Center.

Both point to the same respositories. For convenience I too use Synaptic.

I was thinking more on the lines of the Ubuntu Software Centre being
useful for the new Ubuntu user as it's laid out in an easy to navigate
sections. Synaptic has the same programs but also shows all the
dependances / libraries that can be confusing when not used to it.

At some point users may need to resort to Synaptic but not all will
ever need to delve into that side of Ubuntu. After all, it's promoted
as an easy to use alternative and on the surface it does just that.

Let the deeper mysteries of Ubuntu be revealed as and when they become
necessary ?

Synaptic is telling you that it is going to install the depends with the program
you want to install. it is not like a RPM where as you have to grab all the
depends to make it work. That is good that you are liking Ubie.