One great way to reduce your waste production is to reduce the amount of pre-packaged food you buy.
Convenience - is how most foods are packaged. You can buy vegetables packaged in one portion packages. Lunch and snack food are portioned and individually wrapped for your convience. As well as the single serving sizes you can also get other sizes - in almost everything! This is all very convenient and makes packing a lunch easy but look at all that extra packaging.
Consider buying bulk instead. Most dried foods like pasta, rice, spices, beans, etc. will keep for a long time. If you have the space it certainly makes more sense to buy bulk - its cheaper too! You can buy larger packages of meat and divide it yourself then wrap and freeze whatever portion sizes you want.
Keep your pantry (or cupboard) well stocked with different herbs and spices (not just blends) and you can easily make your own teas, vegetable dips and sauces as well as many other things that will have your family saying : 'Wow! You made that? - From scratch?' It's really not that hard either - but don't tell them that! Here is a link to an eBook with recipies for making great green teas!
Buy yourself some good recipe books and get to it. Look at cooking as something creative. Get your family involved and make meal time an event. Young kids especially enjoy helping in the kitchen.
When you get away from the pre-packaged foods then you will be eating more natural and healthly foods. You will eventually find yourself choosing foods that have less processing, additives and packaging which is good for everyone involved.
Choosing environmentally friendly, healthy foods now will leave an impression on your children and they will adopt your healthy, environmentally friendly food habits.