To ensure the most reliable seals, you should always use jars with two piece lids. The jar itself can be reused. Check each time to be sure that there are no nicks in the rim. The screw band (which holds the lid in place during processing) can also be reused as long as it is in good condition. However, the lid should only be used once.
I give canned goods as gifts, and request that people return the jars, to be reused. I have found that most people do actually return them. I knew one woman who would even tell people, "if you don't return them, you don't get a gift next year." I have never gone that far.
Standard jars have a mouth that is about 2 1/2 inches in diameter. Wide mouth jars are about 3 inches. If you are filling the jars with something large (peach halves for example) the wider mouth can make it easier to get the food out.
Plastic Storage Caps that are made to fit on the canning jars can be handy after you have opened your jar and you want a convenient lid for storing your open jar in the refrigerator.
Canning Jars with Wire Clamp Lids may have been the most reliable jars at one time, but they are not as reliable as two piece lids. Research shows that you are less likely to get a proper seal with them. Further more, since they do not have a safety button, you have no way of knowing whether or not the jar is sealed. These jars are nice for storing macaroni or dried beans. As for canning with them; why take a chance if you don't have too?
When I was a child, I knew a woman who would reuse jars and lids from the grocery store. I strongly discourage this. These were not designed for home canning. I suppose this would be a little less tempting today, since most everything in the grocery store is plastic.