The thing nobody tells you about placemats is that the cheap ones slide around the second you put a plate down, and then you spend every dinner playing a weird game of keep away with your own cutlery. A good set sits flat and stays put, and that alone is worth paying attention to before you look at color or pattern. It sounds minor until you are chasing a mat across the table with a hot bowl in your other hand.
They are not the answer for every table, though. If you have got a table you actually love, old wood with some character in the grain, a marble top you like looking at, placemats can end up covering the best part of the thing. And if your household eats fast and messy, small kids, big elbows, placemats mean more pieces to wash instead of one tablecloth you can just pull off and shake out. There are nights where a cloth is just less fuss.
What separates a mat worth keeping from one that ends up at the back of a drawer comes down to how it is made, not how it looks in a stack. Woven ones should feel dense under your fingers, no gaps you can see light through, with edges that are properly bound rather than just melted or folded over and hoping. Cork and bamboo ones need a bit of weight to them, thin ones warp the first time they meet a wet glass. Hard mats should have a finish that feels sealed, smooth all over, not just on top where you can see it. Run your thumb along the edge in the shop, or wherever you are buying them, and if it catches or feels rough, that is exactly how it will feel in six months, only worse.
These earn their place most in homes that actually use the table every day, not just for show. A rented apartment with a table that has seen three different owners' worth of scratches, a family kitchen where breakfast and homework happen in the same spot an hour apart, a place where you want some protection without committing to a full cloth every time. They are good for summer too, something about a woven or linen mat feels lighter than a cloth once the weather turns warm, and they wipe clean faster when you are eating with the windows open and things get knocked about.
Before you buy, measure your plate across the widest point and make sure the mat gives you at least two inches of clearance all around, otherwise the whole thing disappears under the dinner.