Paper bags are a nice alternative to plastics that are detrimental to our environment. Since paper bags are light, you can carry them easily. Even with a lunch box inside, the bags will be light compared to others. Where some of the paper bags are without handles, some do come with them.
You should have a couple of lunch bags for yourself and your family members. The vertical bags are really helpful in terms of carrying lunch and other stuff.
Instead of monotonous simple bags, you can choose something with writings and pictures. The following image will give you an idea.
If you think it is not possible for you to carry a bag without handles, then you need bags with handles as shown in the image. The paper handles are not easily tearable.