Several people advised me to download ZoneAlarm as a firewall, and so I did. ONE BIG QUESTION? and the question is a question. Do you want to allow DownloadWare to access the Internet?
Zone Alerm asks you if you want certain programs on your computer to connect to the internet.
DownloadWare is a download accelerator that has ad serving technology bundled into it. In my opinion you should not only disable it's access to the internet but uninstall it because there are plenty of download accelerators that do not bundle adware into their installs.
BTW, ZoneAlarm will ask you those questions quite a bit in the beginning, feel free to ask about the programs it is trying to restrict. It can be confusing.