First of all welcome to Ubuntu and Linux as a whole! One of the things that you'll learn about Linux is that there are lot's of great applications and it is very much up to you which ones you will love the most and use. Any answers here should be taken as suggestions rather than definitive truth.
The only thing I would absolutely insist on installing is the Ubuntu Restricted Extras package. This will install all of your media plugins, flash, java, quicktime related plugins all with one click!
For protected DVD playback see here: Playing DVD's
the applications I tend to use on my laptop are:
Synapse - A quick application launcher that is very responsive, pretty, and actively developed. (in the ppa:synapse-core/ppa repository)
Nautilus Elementary - Makes nautilus look much nicer and simpler to navigate. Also comes with great features like an embedded terminal and CoverFlow (in the ppa:am-monkeyd/nautilus-elementary-ppa repository)
Faenza Icon Pack - A fantastic icon pack. Very subjective though, take a look at it before you try installing it, because you might not like it as much as some people do. (in the ppa:tiheum/equinox repository)
GIMP Image Editor - A free and open source image manipulation software (along the lines of Photoshop, but not quite identical)
Mozilla Thunderbird - An excellent mail / news client. Much simpler and more intuitive than the default Evolution.
Cheese - A webcam application with a lot of cool effects. Kind of like the photobooth all the kids use in the Apple store.
Skype - The Linux version is stable and has the major features you need from the Windows or OS X versions.
VLC - An Excellent video player that can handle any kind of video format with no problem.
All of the above can be downloaded by searching for them in the Software Center unless I have specified that they are available in another repository.
You can add new repositories to the Software Center by opening a Terminal (Applications > Accessories > Terminal) and typing in "sudo add-apt-repository ppa:name/of/ppa" without the quotation marks.
If I haven't specified something like a music player, it's because I think that you should experiment with all of the available ones until you find one that you like! Just go through the Software Center and try out things that look interesting, you can always uninstall them if you don't like them.
Good Luck and I hope you find what you enjoy!