Siehe auch: Billet - card?
(I didn't know what a Billet was, but it's evidently a card.)
I think it's up to you; if you would like to send a card, it would certainly be a nice gesture. Your intuition is right that an online comment is relatively impersonal or commercial, and her local friends probably will send a handwritten note or card. But if you're overseas, I doubt she would feel hurt or offended if you didn't, or if you just sent an e-mail.
No idea whether online guestbooks are common these days; I've seen a few of them, but I imagine it's like anything else online, the people who love everything electronic do it, and the ones who don't don't. It might be more practical for someone who has friends scattered in many places than mostly in their own town.
It may have been Nancy Mitford who pointed out that 'funeral home' is really a euphemism, because it's not really anyone's home, and the deceased person isn't going to keep living there. Something in between the cold impersonality of 'Institut' and the false warmth of 'home' might be nice.