You use Dash (The top left button) and type the name of the application and
after about three letters it appears in a dropdown called HUD. You can drag
ad drop icons of frequently used applications to the Launcher (side panel).
The menu button is gone, but that seems to be happening everywhere. W8 has
got rid of the Start button. What is the world coming to? ;)

I do NOT advise Mint or Mate. You can install Mate in Ubuntu and do not
need to re-install. Mint requires a re-installation which is a waste of
time and messy. Mate itself is not worth it either, IMO. It has the same
look and feel as 10.04, BUT it is based on the defunct GNOME 2 and that
means it is a dead end street. We are not even sure if Mint is going to
continue to support it at this time. They cannot make up their mind and if
that is the case then we can't be sure. In any case we know that GNOME 2
was killed off by GNOME for a valid reason. GTK 2 was losing in
the battle to keep up with features and frustrating programmers. GNOME came
out with GTK 3 to address that problem. GNOME 3 is the way to go. That
means you go with Unity which comes with Ubuntu, GNOME Shell which is
installable in Ubuntu, or Cinnamon which is Mint's other desktop
environment (and the better one), but it is installable in Ubuntu.

I have nothing against Mint. If you were just installing then it would be
an option, but to re-install to get Mate or Cinnamon is drastic and
unnecessary. With Mint you do not get a replacement for Ubuntu 10.04
because Mint has never looked like that. It has always used a bottom panel
with a slab menu and not GNOME's panels and menu. It is only a replacement
if you were a previous Mint user.

You can try Mate in Ubuntu, but I would not bet the farm on it being around
for long. Mint is short on developers and they need to focus on doing one
thing well, IMO. I don't like any of the choices personally. But if I had
to use one then it would be Unity. It is under rapid development and well
supported. It is gaining momentum and has many positive reviews. The
downside is that you need to adjust your habits until you learn to use it,
but with all of the shortcuts, lenses, scopes and configuration options it
is way better than anything else in the GNOME family. Again that is
opinion, but I have used Unity for over a year, since its first alpha and
it has really matured.

I use KDE and see no reason to switch, but I do like Unity. If KDE did not
exist then I would likely use it.