Got fast internet? You could also use the mini iso (only 30MB).
Just do a command line install. Then run this command after the mini install:
That will give you a full blown desktop install. I guess you feel your HP is capable of running Unity.
sudo apt-get install ubuntu-desktop
The mini iso can also be used to install Lubuntu and Xubuntu.
Edit: I took too long to post, this has been covered