Coasters for the surfaces you want to protect
A coaster should protect the surface beneath it without trapping moisture or sticking to the glass.

The mark left by a cold glass is a reminder that a coaster has a small but specific job. It should catch moisture, stay stable and suit the table finish. Thickness and decoration are secondary if water simply runs off the edge or the underside scratches the surface.
Measure the base of the widest glass or mug you use. A coaster only slightly wider than a narrow tumbler may be too small for a broad tea mug. Leave enough room that someone can put a drink down without aiming precisely.
Top and underside
Absorbent materials can take in condensation, but they also need time to dry. A non-absorbent surface may be easier to wipe while allowing water to collect around the glass. Look for a design you can inspect and clean, rather than assuming one material solves every problem.
The underside deserves equal attention. Rough edges, trapped grit or a hard unfinished base can mark a table as the coaster moves. Check it by touch and keep it clean. A soft backing can help, but an adhesive backing that starts to detach should not be ignored.
For hot drinks, use a coaster that the maker describes as suitable for that purpose. A decorative disc is not automatically a heat barrier. Follow the furniture maker's advice for the table finish as well; a coaster does not make prolonged heat or moisture harmless.
Use a few before buying many
Try a small quantity with your usual cups. Notice whether a coaster sticks to the damp base when you lift the glass, rocks on the table or becomes difficult to clean after a spill. Those small annoyances matter more in daily use than a perfectly coordinated set.
Let damp coasters dry separately before stacking them. Keep a few near the places drinks actually land, rather than hiding the entire set in a drawer across the room. If guests cannot find them, their protective qualities will not help.
A holder is optional. On a small table it can consume the space the coasters are meant to preserve. Choose storage that suits the number you use, and replace damaged pieces instead of keeping them only to maintain a complete set.