Your host already Gzipping everything might possibly be a problem (in the compatibility test built into W3TC there’s a check on this, so there must be some configuration that causes problems) but I don’t know why so you’ll need to wait for Frederick on that. If you tell us who your host is, someone may already know.
Apart from the above, if you don’t already have some cache plugin, then yes it is usually worth adding a cache plugin – its faster to deliver a page from cache than to have WordPress build it from scratch every time!
The JS and CSS minification does a lot more than just gzip, but does take a little time to set up right. Depending on your theme and plugins it can make a big difference to load times by reducing the number of files that need to be downloaded to the browser (and setting up to download a file can take longer than actually downloading the file for some small js and css files). It was for this feature that I switched my blogs over from using one of the other caching plugins.