When Tyler was a baby we bought some flashcards with a selection of baby signs and I chose which were most important to us and started with those. There's no magic list or order but we just went with ones that seemed like they'd be most helpful to us.
With both boys we started off with signing "milk", I'd show him the sign while saying "milk", then move his hand so that he was doing the sign then I'd nurse him. (You can also use the same sign when you're feeding the baby a bottle of formula or breastmilk.) I'd do that routine most times when I fed him during the days and soon he was doing the sign himself when he was hungry.
The next one I worked on was "all done" we did this once we were feeding food so that they could tell us they were full and had finished eating. This gives the baby more control over their appetite instead of just feeding until the baby food jar is empty.
Once they got those two and were eating more table foods we introduced a few more: "eat", "more" and "drink". We worked on only one or two for a week or so and then would introduce a new one, making sure to continue using the ones that we had just learned.
After we worked on those for a while I worked on the next set: "help", "diaper change", "please" and "thank you". With this selection of words Tyler could talk to me to tell me what he needed. And in the last 6-9 months we've continued to work with Tyler, adding "yes" and "no" so that when he's really upset he can at least answer easy questions. It really helps me to be able to communicate with him when he's in one of those "terrible two" moments. And he also signs "I love you", that's just plain cute!
We got Tyler to do a little movie to show some of the signs. Keep in mind these are toddler signs, just like toddler's words they are easy for parents to understand but might be difficult for others to understand.
If you're looking for a good place to find baby signs here's a Baby Sign Language Dictionary. When you click on a word there's a description of the sign and what it's used for, a drawing of the motion, and a video showing an adult doing the sign. This link is also on my resources page if you need to find it another day.
Have you heard of people using signs for babies and toddlers? Have you used or do you plan on using signs with your baby? I think they're very useful, even just the few that we know!