Hi,
You definitely want to go with custom fields of the table "product" here.
That will allow to to have filters on them.
And actually, the custom product fields data does display on the right side of the product page by default. They only display in the specification tab if you've changed the "product page layout" from "default" to "tabular".
So the simple solution is to change that setting back to "default".
But you might want to keep the tabular display layout and in that case, it will require some modifications to the "show_tabular" view file via the menu Display>Views in order to move the specifications area from its own tab to the right area as it is done in the "show_default" view file.