The most important consideration when choosing an outdoor rocking chair is the materials from which the chair is made. Several types of metals or woods can be used to build an outdoor rocking chair, but not all materials will be rugged, long-lasting, and attractive. Be sure to consider high quality woods that are resistant to water damage and bug infestations, such as cedar or teak. If you want a metal outdoor rocking chair, consider a rugged metal like iron that has been painted or coated with a waterproof coating, or steel that has been coated or galvanized.
Above all, the outdoor rocking chair should be comfortable, strong, and attractive. The chair is likely to sit in a highly visible part of the yard, such as a front porch or patio, so look for attractive designs and materials. Cedar and teak are both naturally beautiful woods: cedar is a reddish-brown color, while teak can take on more of a yellow hue. The downside to these woods is that they are both fairly expensive, more so than cheaper lumber, but they will last a long time even when exposed to the elements, and will require little maintenance. The attractiveness of the woods is enough to make it a worthwhile investment.
Be sure the outdoor rocking chair is well-built. The chair will sit outside, often exposed to the elements, which means shoddy construction or sub-par materials can mean the chair will degrade or fall apart after a short period of time. Check the joints where different parts of the rocking chair meet, and make sure they are connected solidly; metal should be welded properly, and wood should be glued, screwed, nailed, tacked, or otherwise secured in such a way that the joints are strong and attractive.
Consider different rocker designs as well. The traditional style of rocking chair features curved feet on which the chair will rock, while other more modern outdoor rocking chair designs feature a base with pivoting arms that connect to the body of the rocker. If you are looking for a more rustic, traditional look, go with a wood rocking chair designed in the traditional manner. If comfort, function, and modern aesthetics take precedence over tradition, choose a more modern design that will perhaps accommodate more than one person.
Remember that exposure to the elements will mean the materials of the rocking chair can break down quickly. If you choose metal for your outdoor rocking chair material, make sure it is resistant to water damage. Galvanized steel is a good choice for such applications. Cedar and teak are both resistant to water damage as well as bug infestations; if these woods cost more than you want to pay, consider pressure-treated lumber.