What you want to do is basically creating an Ubuntu derivative (please correct me if I'm wrong).
As long as you choose to distribute free software, the only problem you may encounter is the Ubuntu branding, which has some trademarks. Fortunately, there is a page on the Ubuntu website which clearly explains what you can do and what you cannot do with the trademarks. The page is http://www.ubuntu.com/aboutus/trademarkpolicy. The paragraph you are interested in is this one:
We recognise and encourage the concept of a “remix.” Remixes are
derived versions of Ubuntu, and it is intended that any software and
hardware certifications will apply to a Remix. Therefore the changes
from the official Ubuntu product must be minimal to be permitted to
use the Trademarks. These changes can include configuration changes
through the existing Ubuntu configuration management tools, changes to
artwork and graphical themes and some variance in package selection.
In general, a Remix can have applications from the Ubuntu archives
added, or default applications removed, but removing or changing any
infrastructure components (e.g., shared libraries or desktop
components) will result in changes too large for the resulting product
to be called by a Trademark. Note that if the nature of the product's
divergence from Ubuntu changes, the Remix naming and Trademark use may
no longer apply.
[I've reported what I think may be the answer to you question, however I recommend you to read the full page, just to be sure that everything is OK.]
So, given that the above expectations are met, the answer is: yes, you can create your derivative and distribute it.
If you are going to distribute non-free software, then you might encounter other possible legal problems, but they are related to the software's license, not to Ubuntu itself.
Finally, I also suggest you to read this page: https://wiki.ubuntu.com/DerivativeDistroHowto. It doesn't give you many legal advices (the Trademark policy page I linked above is more complete and updated), but contains some technical notes that may help you during your work.
EDIT: If you are seeking a more authoritative and official answer, I suggest you to contact directly Canonical using the form on this page: https://forms.canonical.com/trademark/