When you see a piece of pottery that you like the first thing I would encourage you to do is talk to the potter about it. We love to talk about and explain our work. Ask any question--there are no dumb ones. We know that most people know very little about our craft and we are eager to help them learn a little more. Some other things to look for are:
Excellent craftsmanship. This is perhaps easier to explain by pointing out some things that do not represent excellence. There should be no cracks in the pot either on the bottom or where things like handles or spouts have been attached to the body of the pot. If the pot is intended to be used vs. just being a decorative piece, the glazed surface should be essentially free of pinholes. The pot should have relatively uniform wall thickness from top to bottom. A "nice and heavy" pot--particularly one with a heavy bottom-- is not a sign of excellent craftsmanship.
Design. If the pot is intended for use it needs to be designed well for its intended use. If it has a spout the spout should pour with no or minimum drips and dribbles. Ask the potter if she or he has tested the pot for dribbling. The surfaces that contact food should be smooth and easy to clean--no crevices where food can hide. A functional pot should be stable so it does not tip over easily.
Use of lead in glazes. It is my opinion that no responsible potter uses lead in a glaze on a functional pot. While lead can be handled safely, few potters have the necessary control or testing capabilities to assure that lead in a glaze will not leach into food or drink that the pot holds. Ask the potter whether or not he/she uses lead-free glazes. If you don't get a positive answer, don't buy. On decorative pieces the use of lead in glazes is somewhat more controversial. Some potters say they can't get the colors they want without the use of lead. Others (and more every day) find other ways to get colors that meet their needs because, not only do they not want lead in their product, but they don't want to have to handle lead-containing glaze materials themselves. Even if a lead-containing pot is sold as a decorative piece, my recommendation is that you not buy it if there is any conceivable way someone might use it for food or drink or growing edible plants at some time in the future. Be particularly careful of imported pottery. Potters in many of the developing countries do have have the same understanding of the toxicity of lead that we do in developed countries and they use lead freely and fire it to low temperatures where it will easily release into food or drink. From my personal standpoint, I have never used lead in a glaze and never will.
Price. Most potters today work for an effective wage of well under $10/hour. Even at that, hand made pottery may seem expensive to you. However, if you want a $2 mug, buy it at Walmart. If you want a special and beautiful mug that you will enjoy using then pay a potter $15-25 for it and appreciate that nearly two hours of work and a lot of care went into throwing, trimming, attaching a handle, bisque firing, glazing, glaze firing, inspecting, packing and selling that mug. Then please do enjoy using it.
Though all the above items are important, by far the most important buying tip is to choose a pot that you like and want to have in your home to use or display.