Typically a wood deck should be stained and sealed rather than just painted with exterior paint. Deck paint is formulated to make a film over the surface of the wood which provides a colored finish while protecting the wood beneath. Deck paints typically contain a water-resistant sealant of some kind, which other exterior paints may not have. Regular exterior paints also create a dense, impermeable coating on the wood, which will peel rapidly because as the wood releases moisture the paint is pushed off the surface.
Deck paints are designed to withstand the wear and tear of foot traffic but unlike stains, which are absorbed into the wood, deck paints dry over the surface, forming a film rather than penetrating it. These are high maintenance finishes which require that you sand and repaint at least every two years. Opaque deck paints are available in both oil- and latex-based formulas and while they're both suitable for your deck, consider your maintenance needs when choosing which one to use. Latex allows the wood to breath better than oils, but in an area that will endure a lot of foot traffic, oil is a more durable finish.
Ideally a deck should be finished with a water-repellent semi-transparent stain. These are not truly stains, but extremely thinned paint which must be stirred before use. Semi-transparent deck stains also contain paint pigments, while true stains need no mixing and are absorbed directly into the wood fibers. An ideal deck finish contains both pigment and protection from moisture and the sun. Opaque stains are best for vertical surfaces where wear and tear is not an issue. For the deck surface, true stains are difficult to work with because you have a very large surface to provide an even coat of stain to, and they may not contain a sealer to protect against moisture. Semi-transparent deck stains act as sealers, allowing you to color the surface with a durable finish while offering some protection against moisture.
Paints and stains are not your only option for protecting your deck. A water-repellent sealer protects the wood against moisture and is easily refreshed each year because you don't have to sand the surface to apply a new coating. If you choose to stain your deck with a true stain, add a clear coat of water-repellent sealer over top to protect the wood and to prolong the life of your stain.