If the word after "a/an" starts with a vowel (A, E, I, O or U), you use "an." If it begins with a consonant (any other letter), you use "a."
For "an insecure place," you use "an" because the word after "an" starts with a vowel, but it refers to "place" (the noun) rather than "insecure" (the adjective). You would say "a very insecure place" because the first letter of the word after "a" is a V which is a consonant.
For the second one, you say "a pizza" because the word after the "a" starts with a consonant.