I don't know what town you are in, but a lot of places in the world right now have seed libraries, usually run out of actual book libraries. You 'borrow' seeds from the library in spring, and 'return' them in the fall (or next year fall for biannual).
Basically you grow the veg, then save the seeds. Save
enough seeds for you to plant next year's crop and give the rest back to the library...
... however, I usually go by the third rule. 1/3 for seeds for my garden. 1/3 for my kitchen. 1/3 to return to the library.
The best thing about seed libraries is that they are free and/or included in your book library membership. If you don't have one yet, it might be a fun project to start with the kids.
Another source would be Seed Savers Exchange (in the US) or Seeds of Diversity (in Canada). You usually need to pay shipping on the seeds sent from individuals, and are encouraged to save and share your seeds in future years.
If you were in town, I could donate some seeds. But right now, seeds traveling away from Canada seem to get destroyed in the mail.
One last source of free seeds - your grocery store!
I say free. Basically you are paying for the food, and just save the seeds before you eating the rest of the veg/fruit. Depending on how much work you wish to do, you can get a huge variety of seed.
Simple seed saving is like scooping the seeds out of squash (BEFORE cooking), drying them, planting them.
More complex include fermenting your own tomato or cucumber seeds.
Even more complex include growing out carrots or potato for seed.
If you like, I can give you long instructions on fun ways to transform groceries into garden. Just let me know.
I don't have kids of my own, but the ones I borrow for labour on the farm, really enjoy transforming groceries into plants.
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