Just received my grandfather's pocket watch, and quite possibly his grandfather's too

[ArcticMoose]

Long story short, my grandmother decided I could have anything watch-related found around the house as it was being emptied. I just got these, couldn't be more thrilled!





Can anyone tell me more about them, or where I can find more information? I've done a bit of searching, but haven't come across any particularly specific information.

The Hamilton could potentially have been my great great grandfather's, since I believe it is engraved with his initials. I'm looking into it.

Besides origin and history, my most pressing inquiries are: What specific questions should I ask a watchmaker before allowing any work on them? Any specific requests I should have, besides the obvious such as leaving original dial and hands alone?

I haven't dared attempting to wind them for fear of breaking them, so I don't know what condition they are in besides the obvious, that the Elgin is missing its second hand.