Reuse the pots you have, return nursery pots to garden centres that take them, sow into paper or coir pots, and use straw, bark or compost as mulch instead of plastic sheeting. Tie plants with jute or cotton twine.
A year of new nursery pots, trays and twine is around 600 g of plastic for a keen gardener. Certified compostable mulch films (Novamont's Mater-Bi, EN 13432) exist for growers, but for a home garden organic mulch avoids the question entirely.
The catch: biodegradable mulch film still leaves fragments in soil while it breaks down and depends on soil temperature; coir pots are shipped long distances.