10-09-2016 08:29 AM
Welcome to the Lenovo Community !
According to the Lenovo specifications your system can use a maximum of 8 GBs of memory. With your present configuration you can easily add another 4 GB module to your empty socket for a total of 8 GBs installed.
Personally I like Crucial memory as I have never had a problem, they have decent prices and they guarantee compatibility. Other members here may have other preferences. Here is the result of my search.....
For future reference here is a link to the Lenovo PSREF specification sheets for the Z580 that you might find useful in the future. The Z580 starts on page #99.