*.rpm ("Redhat Package Manager") is the package format used for Red Hat and distributions based on Red Hat. In addition, some distros not directly based on Red Hat also use *.rpm format.
*.deb is the format used for Debian and distros based on Debian (of which Ubuntu is one). For your Ubuntu system, you would need *.deb.
In most cases, you should be able to find the software you need already in Ubuntu's repositories (commonly referred to as "repos"). I think it's now called the "Software Center."
If you can find the software in the repos, it's better to get it from them than to download it from random websites, as it gets tested before it goes in the repos. This article gives a good intro to package management on Linux: http://www.howtogeek.com/117579/htg-...work-on-linux/