Biblical refers only to the Hebrew idiom used in the Bible. Classical probably makes more sense, because it contains all of the rabbinical writings used during ancient times. That leaves you with a much broader vocabulary (the vocabulary of the Bible is noticeably sparse, although there are a lot of words we still don't know the meaning of).
I actually fully agree with that. That's why I prefer calling it Classical Hebrew, but some people may prefer Biblical, hence what I said.
Okay, but keep in mind that Rabbinical Hebrew grammatical forms sometimes differ from Biblical. Your first Hebrew book will (most likely) teach you something distinctively "Biblical" rather than a broader "Classical" Hebrew. (I still consider myself a n00b in Hebrew, and I'm focusing mostly on the grammar to get the forms right so I can plug in vocabs.)
A few random differences I noted from Hebrew chapter of Ancient Languages of Syria-Palestine
* anoki as first person pronoun disappears rather completely in RH
* masculine plural -im changes to -in, but this is dialectal rather than historical. Archaic Hebrew in Judges 5 contains -in plural as well
* second person feminine plural imperative disappears and the masculine takes over
* hop'al sometimes appears as huph'al, in analogy of pi'el - pu'al
* hitpa'el sometimes appears s nitpa'el, in confusion with nip'al
Though I wouldn't know anything about the Coptic verbal forms (yet), I have been quite interested in Coptic for sometime (and by proxy Ancient Egyptian).
As for the Coptic verbs: the verb stem never changes. This is a good news. It does have more tenses but formed rather simply by adding a few particles here and there. e.g:
Present: ti.nau (I see) k.nau (you (sg.) see), f.nau (he sees), s.nau (she sees) etc.
Future: ti.na.nau (I will see), k.na.nau, f.na.nau, s.na.nau, etc.
Perfect: a.i.nau (I saw), a.k.nau, a.f.nau, a.s.nau, etc.
Aorist: sha.i.nau (I saw), sha.k.nau, sha.f.nau, sha.s.nau, etc.
As long as you remember what prefix to use, Coptic verbs should give you much less headache than other Semitic ones. (Though the noun strings can drive you crazy, with that goddamn (e)n- prefix which could mean so many things...)
And I'd appreciate if anyone could give me a tip about how to deal with the hieroglyphs. I don't want to spend five minutes drawing a vulcan or owl to write a single grapheme.