Naïve solutions

Unsorted array

Idea: put new items at the end of the array; when deleting, fill the gap by the last item
Advantages: very simple; insert in $O(1)$
Disadvantages: extract-min takes linear time (we have to search the whole array for a new minimum)

Sorted array

Idea: keep all the items in a sorted order
Advantages: still simple; extract-min in $O(1)$
Disadvantages: insert in $O(n)$