My site breaks after I enabled minify / cache plugins and combined CSS/JS files

Using CSS/JS minify option require manual configuration and good knowledge of how all of your plugins and themes work. A lot of plugins and frameworks files used in themes does not allow minification or combinations of its files because this will break site entirely. If you are planning to use minify option you need to manually define exclusions, disable minification for plugins that breaks and properly configure minify plugin options. We does not recommend you to enable JavaScript minification or combination, because this leads to unpredictable issues with 90% of plugins and themes (this does not mean that plugin or theme have any issues, this just mean that minify feature of your cache plugin does not support some frameworks used in this plugins and themes).

You can find additional information about minify configuration in W3TotalCache plugin here:

https://code.tutsplus.com/articles/configuring-w3-total-cache-advanced-minification-settings--wp-31043