Don't follow the link - it is american - totally different to BSL / Makaton.
A friend had a similar problem and started with just two signs, one was drink - make a drinking motion, the same as if you were in the pub and asking someone accross the room if they want another.
I can't remember what the other was, but basically if he wanted a drink he had to ask for it. After about two weeks he decided it was easier to talk than sign. Assuming you and dc are both hearing you are going to use this as a communication system, not a language so say the word at the same time as signing.
It really is useful - a friend who is a BSL interpreter taught her kids BSL before English. Very useful for me when I went round and could hear her vacuuming but she couldn't hear me knocking, I could just sign through the window at her 4 year old "go get mum".
A lot of signs that a young child will use are ikonic - ie they look like the object, so drink - your hand is like it is holding a glass and moving to your lips.
Hello - you just wave 'hello' - hand goes from left to right in an ark
Hungry - put your hand flat on your tummy with the thumb upwards, leave yoour little finger across your tum and move your hand down so your thumb is the furthest away - sort ofthe opposit of opening a lid.
food / eat - put all your fingers of one hand on the thumb of that hand and move it to your mouth
some not so ikonic but useful
mum - put your hand into the girl guide / scout saloute - middle three fingers up, thumb holding little finger then tap your head just above your temple
dad - both hands in similar position but with ring finger tucked in as well and tap the fingers on one hand onto the fingrs of the other hand making the fingers into a cross.
toilet - there are numerous signs for toilet and one only used by small children - put your hands together with the fingers intertwined - do you know the "here's a church, here's a steeple"? put your hands in the church position. In small children this is often accompanied by hopping from one foot to another - it obviously also means 'my nappy is wet'
good luck