Every modern operating system can open a .ZIP file without external help. Just double-click on it. If that fails for any reason, there's no shortage of free archive managers (and file managers) that can do it, for example 7Zip. Oh, and last time I checked, WinZip was shareware. You don't have to pay for it -- not at first, anyway.
ZIP is quite literally the most widely supported archive format. Any other option would be less flexible.