I need to find a good (reliable) Zip program for my MacBook Pro (the last one I downloaded installed Spyware on my system...so now I'm "gun-shy" about downloading ANYTHING to my system)

There are many free unzippers available from the Mac App Store. Just search for: zip.

I would try Stuffit expander. Stuffit is well respected and getting it from the App Store should mean no adware.

Mac OS X actually has a built-in ZIP tool that can both unzip files and zip files. However older versions of OS X do not cope well with password protected zip files and it maybe some of your zip files also use newer options your old operating systems correspondingly old zip tool does not support.

I would therefore echo the suggestion of Illaass and recommend you get the free Stuffit Expander tool.

For what its worth you now can actually buy a version of WinZip for the Mac, see http://www.winzip.com/mac/en/index.html I have not used it as I find the built-in zip tool in newer OS X versions along with Stuffit Expander sufficient. I have also written an Automator workflow which allows me to create password protected zip files.

Check out The Unarchiver (free)

https://itunes.apple.com/us/app/the-unarchiver/id425424353?mt=12

It will open common formats such as Zip, RAR, 7-zip, Tar, Gzip and Bzip2. It will also open many older formats, such as StuffIt, DiskDoubler, LZH, ARJ and ARC. It will even open other kinds of files, like ISO and BIN disc images, some Windows .EXE installers. The list is actually much longer - see the program homepage for the full list.