It's been said already but the Baby Signing Time is great! We're not tv people but we do watch the videos. It's amazing how much my children learned from it. I watched every show with them - repeating them over and over and over again.... :) but we learned together.
My now three year old really "clicked" with signing at about 16 months - she was signing before then but I wasn't doing it enough so she was slow to pick up on it as well. We had all the basics which was great but expanding it was amazing.
My now 15 month old is fully versed in sign. (Both are speakers as well.) She signs as we read books the different animals, she signs when we're leaving the house car. She signs when she sees a baby or someone wearing a hat or glasses. She tells me when she's tired, sees or hears a baby crying, wants milk, water, juice or to eat. She knows different peoples names and can identify toys.
It's amazing how much she communicates to me and how much I can understand. Her vocabulary is no where close to being able to match her signing. She does vocalize but there is no way I'd understand it all.
I credit the 2nd childs huge advantage to me signing more, her sister signing and the videos which I started much later for my first.
There is a difference between some signing books/videos between ASL and baby sign. I prefer to try to teach the ASL and work with the child from there. For example to sign water take three fingers (touching your pinky to your thumb) and tap on your chin. My now 15 month old has been doing this sign for a very long time but she doesn't have the coordination to get the three fingers up. Her version is one finger up waved near her chin/cheek. We know it means water.
I would recommend whatever method you do use try for the ASL and adapt as your child does.
Good luck with it! It's amazing to see how well a small child can communicate at such an early age.