Well... Depending on what material you are working with, you have a choice of steel or carbide. Taps come in bottom, plug, and taper.... Which depending on your hole depends on the tap to use.
Most common for home type / garage use and what come in sets are plug or maybe taper, and are made of steel.
I would say buy new because a tap & die are a perishable item, they will get dull and if you aren't careful you can break a tap in your hole. You can search for used, but unless they "look new" I probably wouldn't even bother. Well, the only exception to that would be for pipe threading as black pipe is pretty soft compared to the threading dies.
Don't forget to get some cutting fluid. Or you can use WD40 if you aren't going to be doing much or just don't want to have a bottle sitting on your shelf for 20 years.
If you have a project where you know you will be cutting a bunch of X threads, order just those taps and order one or two extra because you more than likely will break one.
Also if you kit doesn't include a chart, you can find them on the internet. They will tell you the side hole to drill for a particular tap.