The best rule in English is that you should ignore spelling for purposes of pronunciation and ignore pronunciation for purposes of spelling, as these two things each have their own separate stories. You must learn each one separately by rote, not attempt to infer one from the other.
Sandhi effects have nothing to do with letters. They are purely phonologic in origin, so only sounds count.
So eunuchs, Unix, Europe, Ulysses, eustachian, Oaxaca all begin with consonants, while honor, honest, hour, huerta, our, umbrella, ylem, Ysidro all begin with vowels. Words like herbal and historical can vary.
And not all sandhi effects are the same, either. Just because we use the same pronunciation for an in both an apple and an eel doesn’t mean we use the same pronunciation of the in both the apple and the eel; with the eel, there is an extra glottal stop after /ði/, so /ðiʔˈil/.