Bibs-- Mimi the Sardine bibs are organic cotton from Europe, coated with acryllic and guaranteed free of BPA, phthalates, and other chemicals. When our son was younger we would keep one in the diaper bag and then rotate the others at feedings. We would just handwash them in the sink after each meal and hang them on the towel rack to dry. They come in a variety of patterns and prices, all easily available on Amazon.
Placemats-- Mimi the Sardine makes placemats that match the bib designs, and can also be found online at retailers like Amazon. Like the bibs, they are organic cotton with a food grade acryllic coating on top serving as the stain resistant coating. We rinse them in the sink after every meal and they're usually dry in a couple hours.
Napkins-- You can make your own cotton napkins to reuse and pick patterns out for the different seasons and holidays. If sewing isn't for you, you can find great deals on 100% cotton napkins in Bed Bath and Beyond's clearance center. I got two 8 pack cotton napkins in a variety of vibrant colors on separate occassions. They were $5 on clearance, which made them $4 plus tax with the 20% off coupon, making each napkin a little more than 50 cents each. They are easy to wash in the laundry machine and cut down on the wastage of paper products.
Plates-- When my son was younger I would serve his food in pyrex glass bowls or stainless steel bowls. You aren't suposed to heat plastic so I never had any plasticware for him because I didn't want to serve hot food in plastic either. I never let him handle the glass bowls. I currently just use stainless steel plates and bowls for my child now that he is handling the dishes and can throw them. You can buy plates with sections built in that make meals a little more interesting for older children as they finish off what's in each compartment.
Cups--For cups, I use small stainless steel cups from India and Klean Kanteen cups. The taller Kanteen cups are too large for a small child to drink out of himself but my son has no problems feeding himself water from the smaller cups. Klean Kanteen makes fantastic 12oz stainless steel bottles that are responsibly made in China and guaranteed to be free of BPA, Phthalates and lead. I never leave home without one and my son easily drinks from them at restaurants instead of wasting a plastic child's cup. We never used a sippy cup but Klean Kanteen has BPA free sippy cup adaptor tops that fit on the 12 oz bottles. You can buy a regular cap to use the bottle as a regular water bottle when your child is older too. Unlike plastic and aluminum bottles which can leach products into your water, Klean Kanteens are just made of food grade stainless steel and they don't have any coating like other stainless steel bottles so to me, that makes them well worth the price.
Silverware--We just use stainless steel silverware but when our son first started eating solids at 6.5 months we used the Playtex Toddler Spoon and Fork set. The handles are pink plastic that is BPA free but the actual spoon and fork are stainless steel. When he was a little older we used the Oxo Tot Forks and Spoons, which are BPA, Phthalate and PVC free.
Tablecloths and chair covers-- When my son was old enough to sit at his table and chair, I just used old towels to cover the white IKEA table and chairs and protect them from stains. They easily wash and do a great job serving as a barrier between spills and the furniture. I made chair covers for the backs of the chairs out of old t-shirts. Look for a tutorial on those in the upcoming months on Wading Through Soup. New posts every Monday and Thursday.