Good question. I'm glad there's a guy called "Dr. Grammar" to come to the rescue.
"Use a before a consonant sound; use an before a vowel sound. Before a letter or an acronym or before numerals, choose a or an according to the way the letter or numeral is pronounced: an FDA directive, a U.N. resolution, a $5.00 bill" (Merriam-Webster's Dictionary of English Usage). Please note: This is the basic rule. For a more thorough presentation of the complexities of using a or an, see the source cited here."
So a/an depends on the sound, not the letter. Thus:
An uninhibited young womam ("uh" sort of sound)
an mce extension (an Em-Cee-Eee extension)
Unit is tricky, but is "A unit" according to this thread:
"The reason you have to use a instead of an is the "u-sound" you find at the beginning of words like use, you, European, etc, is, from the phonetic point of view, a semi-vowel, that is, a sound which ressembles a vowel but is used as if it was a consonant. And the same goes to the w-sound (in words like wave, wagon, etc.)"
By the way, I regularly use wordreference (cited above), which has great forums for language learners to help each other with this kind of thing.