The size of your disk isn’t usually a huge factor. It is mostly so it is comfortable for your dog to wear, and doesn’t get in their way when they run or play. Obviously, a huge tag for a Great Dane would look out of place on a Chihuahua.
You can often pick a choice of small, medium or large. It still has to be large enough to hold all of the relevant information, but most engravers or printers can often change the font size to suit.
If your dog has a lot of data to put on their tag, such as medical needs, opting for a tag which can be printed on both sides or maybe even having a second tag on there could be a good idea.
This isn’t strict, but ensure the colour of your tag doesn’t affect how legible the writing and information is. Dark font on a black disk would be pointless.
Most offer a choice of white or black, which are probably the best for all-round visibility. Some metal tags are left as their natural silver or gold colour and engraved as opposed to printing the information, so check this occasionally for wear and to ensure it is still legible.
Metal is the most common. This is sturdy, quality and less likely to become damaged than plastic, but double-check it won’t irritate them or become tarnished.