Aw. I'm sorry you were shy. I think it's awesome when people ask questions like these, instead of simply going with whatever a medical doctor recommends.
I would consider learning ASL as soon as possible. Even if your kids aren't deaf (and you're right, hereditary deafness means that is a good possibility), their kids might be, and the best thing you can do is be a language model for them right off the bat. If there's deafness in the family you may as well raise them bilingually even if they are hearing.
If they're deaf, well, you absolutely want to start out signing to them. This way they are able to acquire language naturally the same way that hearing babies do. Studies show that deaf babies in ASL households acquire language milestones at the same time and in the same way as hearing babies in spoken-language households.
So the first thing is to raise them learning a language naturally. It might even be English depending on their level of hearing loss, but ASL is fine too. Either one develops the brain normally. This is what seems like an obvious step but is the one missing from most deaf children's lives, and is what causes so many problems later on.
After that, there are really a lot of different options. You will probably want to consult audiologists and speech therapists about how best to start teaching a deaf child English (including speech therapy, hearing aids, speechreading, etc.), but if you are raising them with ASL, it is vitally important to find specialists who do not reject signing. Many of them do. If you connect with your local deaf community (and especially if you have a deaf child!), you can probably find people who will work with your signing child.
I believe in giving a deaf child every opportunity to learn every way he or she can. At some point the kid might say "screw speech therapy, I'm just going to sign" or "screw signing, I want a cochlear implant," but the important thing is that they are able to make a choice based on having all the options.
Definitely reach out to the deaf community in your area, and consider ASL classes, or there are some very good programs like
Signing Naturally where you can study at home. (In-person is best for a three-dimensional language, however.) You could of course wait until you have a child, but that's usually not the best time to be trying to learn a language.
That's my initial advice, and please do PM me if you ever have any questions since I'm not guaranteed to remember to check this thread. (A little birdie was nice enough to alert me to it.)
EDIT: Okay, I forgot where Tegid lives, so this advice is pretty U.S.-centric and sorry about that. Obviously it would be LSE not ASL and my points about the resources may not apply. But the basic premise is still the same about the child acquiring a language naturally first, which would probably be sign.