I think when they are toddlers all they need are crayons, stickers, an aqua doodle, some plain and coloured paper and the odd painting session and playdoh . As they get older you can start doing more detailed crafts with little bits and pieces. Ours has evolved over the past 5 years (DD1 is nearly 6) and has all sorts in there, googly eyes, glitter glue, bits of material, fat markers, skinny markers, big crayons, little crayons, stamp sets, hole punch, beads, ribbon, craft scissors, old cards/envelopes - you end up with so much from people buying them stuff over the years and from birthdays/Christmas (art stuff is a great stocking filler), so don't feel you have to stock up much now, just get the box started and put a few things in there.
All kids are different regarding 'interest level' in crafts, but certainly you can introduce it from around 18 months, my nearly 2 year old will happily scribble in her high chair for a good 15/20 mins, I think if they are just breaking crayons on purpose I would stop the activity - my 5 year old loves crafts but probably didn't have much of an attention span for them as a toddler.