One thing you need to know, vendors of commercial systems try to do the thinking for you. Windows, MacOSX and Ubuntu are such vendors. For Ubuntu, you will have to remove all the apps that you don't want and install your own.
If the apps are available you can install them from the software-center program, download them from the Internet or compile them from source. The source will end in .tar.xxx.
If you want to choose what apps you want, use a system similar to Archlinux or slackware. A simple that allows you to choose the programs you want to install. In fact Ubuntu based systems do have an option during the installation that allows you to manually install apps of your choosing. This does not compare to the previous two.
In your situation, either see if there is a Ubuntu distro that has what you need, manually remove what you don't want or choose a Ubuntu flavor distro like xubuntu or lubuntu that don't have such a bloated system and make your modifications there. Just make sure you do not remove what might be important.
If you are looking for an elementary Ubuntu system, choose Ubuntu elementary which is the actual name.