Question: I would like to know when is a good time to start teaching your baby sign language. I heard they won't start signing back to you before 6-7 months so starting before 3 months might be pointless. Any thoughts on when you think would be a good time to start for your sake as well as your baby's?

Answer: 
Just do it as normal all the time.

They pick up everything all the time.

That is how children learn by seeing, hearing and experiencing things.
We incorporated basic signs with our children pretty much right after they started opening their eyes (i.e. around 1 month) and coupled it with words. We are not proficient in sign language, we limited ourselves to 'eat', 'drink', and 'more' and was done with a deliberate goal towards the long game and had demonstrable benefits for us.

Our kids are now 3 & 5 and are 3 year old will sometimes fall back on his sign language when he's extremely upset and that's where the benefits really show. Temper tantrums can make forming his thoughts into words all the more difficult, so having a few signs to help him say what he wants can be very helpful for him to convey his desires without words.

He even uses it at bedtime as his way to say, "I love you," and it is the cutest thing ever.

So to summarize, anytime is fine, but I will say there are benefits to be had. It probably won't prevent temper tantrums from occurring, but it will make them a little easier to handle.