You should save the selected values through the rune_save() function. Where should the selection be saved? It can be anywhere in the DB. If the selection is related to the post being saved, post meta makes sense, so update_post_meta(() would be correct, but the parameters currently used in your code are undefined. Don’t rely on the global $post, it may not have the values you think it does.
I don’t know what meta key you want to use, I’ll use “apo_runes”. It’s a good idea to prefix meta names with something unique in order to not conflict with other plugins. You can save the selected tag with this:
update_post_meta( $post_id, 'apo_runes', $_POST['runeselect'] );
Note that this is a terrible example because we should never put user input directly into the DB. The value in $_POST actually needs validation and sanitation. What I’ve presented will suffice temporarily, but you need to implement proper security before going live.
When you output the field’s options, you can get the currently saved value if it exists with get_post_meta() and use it in the selected() function so that the previously saved option is preselected for the user. This part is optional. Without this, the first option is always selected.
You can also use get_post_meta() anywhere on any template to get the saved value. You only need the associated post ID. If you are in the loop, get_the_ID() will return the current post ID.