Just a reminder that if you do get toothpaste, be sure to get one specified for toddlers. (Older children and regular toothpaste have flouride which is not meant to be ingested on a regular basis.) We also use this strawberry/banana one that comes in a light blue box and has a pic of the baby in front.
My son is past two so I took him to a paediatric dentist a couple of months ago for a proper check and he told me that while brushing with a toothbrush is good practice for them to learn, you could start with young babies by using your finger wrapped around a piece of wet gauze (wet with boiled cooled water if your baby is really young ) and no need for toothpaste.