I am trying to simply make a list of links to k2 articles in a category. From menu settings when I select Category and try to configure Basic Options/Layout Options I am unable to because they are greyed-out and inaccessible. What am I doing wrong? Thanks ahead of time for any help.

All settings for K2 are basically handled through the category. The menu item to a category fetches the options you have setup in the category. The options will stop being grey once you select multiple categories to show through your menu item.

I would recommend you watch the tutorial videos below in order to familiarise with K2.
getk2.org/documentation/k2class2012