Why you should know: The ‘a’ vs ‘an’ conundrum is not about what letter actually begins the word, but instead about how the sound of the word starts.
For example, the ‘h’ in ‘hour’ is silent, so you would say ‘an hour’ and not ‘a hour’. A trickier example is Ukraine: because the ‘U’ is pronounced as ‘You’, and in this case the ‘y’ is a consonant, you would say “a Ukraine” and not “an Ukraine”.
Tip: when in doubt, sound it out(loud).
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Actually Khrushchev. For some reason, х gets converted to kh. The rest is slightly stupid but at least understandable why it is so - щ was historically ш+ч, thus sh+ch (this pronunciation is still normal in Ukrainian, but not in Russian anymore), and the ‘e’ is just based on the usual spelling.