We taught our first son to sign for the same reasons you are thinking about it. His obvious frustration. The first sign we taught him was "milk". I started when he was around 8 months and he did it on his own around 10 months. It helped immensely because I was never sure if he was hungry or wanted something else. Once he could ask for milk, I knew what he needed. Around a year we started teaching him tonnes more (bath, more, swim, eat, please, thank you etc etc) and he learned about 50 signs alltogether by about 18 months.

My daughter is now 11 months old and she knows "more, milk, eat, tired, all done and bath". She doesn't do them all herself unprompted, but recognizes them, and will copy me if I do them to her.

If you start now, thebest one to start with is milk. Do it every time you offer him his milk (either formula, or breastmilk, whichever you are doing). He'll figure it out probably in a couple of weeks. Eat is another good one that i use for solid foods (anything that is not "milk"). My daughter picks them up pretty quick, after a couple of weeks of consistently doing the sign every time I say the word.

I've included below a great website for learning the signs yourself. You look up the word you want and a little video of a woman doing the sign pops up.

Feel free to email me if you have more questions. We love signing!!
Good luck!