I use a/an depending on the *sound, not on the letter.

thus, if you say FBI as eff-bee-eye (and who doesn't), say
an FBI agent. (of course, if you expand these sorts of acronyms you end up with 'a Federal Bureau of Investigation agent'.)

the silent h, which isn't very prevalent in Midwestern speech, presents a similar case. a historical event.. an 'istorical event.