Instructions
Decide what your main use for the set will be. If you are going to keep the set on display in your home, your main priority will be finding the most aesthetically pleasing materials, but if you are going to be transporting the set a lot, you should look first at durability.
Look for the right set for display by deciding where you will have the chess board. Find a board with wood that will match or accent the materials of the room, or using another neutral material such as glass or stone.
Find a good set for convenient travel use by shopping around for sets that are good quality and also portable. There are a number of options for quality wooden sets with magnetic pieces that are travel-sized but also look great on display. Make sure that travel-sized sets are still comfortable for you to use regularly and not too small.
Use a weighted plastic set if you need a set that is durable and transportable, but you don't like the feel of a travel set.
Select chess pieces to match the board. If you are buying the board and the pieces separately, make sure that you check out the proportion of the piece to the square. While proportions are a matter of preference, if you will be competing in any sanctioned tournaments, there are specific regulations you will have to follow there.
Determine the quality of your pieces overall by specifically examining the detail on the knights and the king's crown. These are the most aesthetically valued pieces on high-quality sets.
Match your practical purposes and your budget. Durable, transportable sets can generally be found at affordable prices, but even high-quality sets will range from extremely expensive to fairly affordable. Know your materials specifications and look for the best set you can afford within those limits.