I grew up using those flimsy paper napkins, the square ones with the nubby texture. I suspect maybe everyone who grew up in the 80's used those. If you were lucky they were white. If you were unlucky they had images of geese in baskets on them, or some such nonsense. At some point in my adult life I realized that using cloth napkins is really easy and I switched to using those all the time. They feel nicer and they don't waste paper and they can generally handle messes a lot better. Have you tried using those thin paper napkins while eating barbecue? And don't even get me started on the paper napkins used in Mexico. They actually melt in your hand as you use them. You need about 14 of them to make it through a plate of enchiladas.
At our house we have The Napkin Basket. It looks like this:
It is full of cloth napkins that I've picked up in thrift stores and garage sales over the years. There must be at least a dozen different patterns and sizes in there. (It's only partially full in the photo.) There are sets of 8, sets of 3, big ones, tiny ones, flowered ones, striped ones, ones with appliqued images of extreme sports (really), and one that was hand-embroidered with what I thought was an alien but turned out to be a potted plant (how disappointing). I think we all have our favorites. Because I pay so little for them I make sure to always have lots so we don't run out. I just wash them with our regular laundry and because they are especially easy to fold the kids often help to fold them. I put them in the kids' lunch boxes and pack them in my snack bag when we go out. If one gets lost it doesn't matter because they aren't fancy. They are so small that it never feels like they add anything to our laundry burden.
If you want to make the transition to cloth napkins full-time I would recommend buying a bunch at a thrift store. Look for napkins that are 100% cotton because the ones that contain polyester are too water-repellant. Thrifted napkins might not have a tag on them so just feel the fabric and see if it feels like cotton. Polyester blends will be slicker and less wrinkled than cotton. Wrinkled is okay for everyday napkins! By all means, don't feel like you should iron them. And you certainly don't have to have matching sets. Start out with at least a dozen and see how you like using them. Then build up your stash as you come across good deals.
You usually don't have to change napkins for every person at every meal. If the breakfast napkins aren't dirty I will leave them out for lunch or dinner. When we have house guests I give everyone a napkin ring with their name on it so we can all keep track of our napkins. I have about a dozen napkin rings that I picked up in thrift stores and they are all different (there are roosters and pigs and sheep and birds, etc). Even little children who can't read can keep track of their own napkin ring. I was surprised when Little Sister (age 2) was able to identify the napkin rings of all 8 of us when my in-laws were here over Christmas break.
So here is a quick summary for switching to cloth napkins:
1) Buy em' cheap (used is great)
2) Buy lots
3) Avoid polyester