Hi Melanie,
Not a Mom here but I am currently a speech-lanugage pathology graduate student and have some experience clinically with child language developement and baby signing. Of course, I will just be interjecting some personal observations here and will be careful not to draw conclusions.
I think "baby signing" is a great idea to start to use with your middle child, and your youngest for that matter! There is evidence to suggest that signing with very young children doesn't necessariy improve intelligence but is a GREAT way to facilitate communication in a non-verbal way. Studies that have been done show that signs are a great way to bridge the gap between symbolic expression and oral (talking) expression. Because you say your oldest did not really begin speaking until 3 years of age, I wouldn't be too worried about this child at all. Many children just have a learning difference and some just take longer to get the words out. Because you seemed to express concern that he shows frustration making himself understood, then this signing is a great way to give him a modality of communication that will be easy to understand by you the parents, as well as other family and siblings with minimal instruction. If no improvements are made within the next year I might advise visiting your pediatrician to refer for a speech language evaluation just to rule out any possible true delays. Anyway, using the baby signs is a great way to continue to bond with your little one and could very well help him transition to more verbal language. I have some articles you may be interested in however they are in Adobe PDF format. I'd be happy to send them to you if you want. Also, many community centers, YMCAs, local libraries, schools, etc. offer sign workshops. And, there are many books and manuals on the market for your use. In general, it's a pretty informal system to teaching signs to young kids. Just a note: you can make up your own signs for common objects in the childs everyday life and for activies like eat, more, up, down, etc. Just be consistent in their use; or, you can teach actual American Sign Language vocabulary words or baby sign words and gestures from books that are an adaption between ASL signs and more symbolic, "made-up" signs. Either one is great.
Sorry this message ended up so long but I can go on and on about these topics. If you have any other questions I'd love to discuss, and again, obviously, I'm just here to provide my own personal knowledge and interest...
Hope this helps! Good luck!
Catie