Skis, boots, and poles
Avid skiers may own several sets of skis for different types of terrain and conditions. But if you're just getting started in the sport, you don't need to be too specialized. You'll need a good set of all-mountain skis first. These are designed to work well in a variety of conditions, and are very well suited to the groomed slopes that you'll encounter most often when you're learning.
Instead of going to a ski shop to buy skis to start with, it's a better strategy to rent skis when you're beginning. Typically skis for beginners and less-experienced skiers are shorter, which makes them easier to maneuver and turn. But as you improve, you'll want longer skis that give a smoother ride as you go faster. If you rent, you can gradually change the skis you use as you improve without investing a lot of money frequently in new boards.
Renting boots makes sense as well. Let your feet and lower body get adjusted to the sport before you make a big investment in boots. Simple aluminum poles will suffice for quite a while, and are readily available to rent.
Clothing: Base Layers
Comfortable clothing is important. A cold, wet skier isn't likely to have much fun on the slopes--good base layers are an important part of keeping you warm and dry. Start with quality ski socks. Your boots will keep your feet warm, so you only need a single layer. Most skiers prefer relatively thin, calf high ski socks. They won't bunch up in your boots and cause pressure points. Choose a synthetic material that wicks moisture; silk and capilene are excellent base layers. Consult with a local ski shop, as they will have the best idea of the weight, or thickness of base layers, you'll need for your area.
Clothing - Outer Layers
Ski pants are very important for your comfort. They will keep your legs dry, unlike cotton fabrics like denim, and will block wind too. Ski pants are designed to be easy to put on over your ski boots too. Ski pants are available either lined or unlined. Don't choose lined pants unless your area is particularly cold. Again, it's a good idea to consult with a local shop that knows conditions in your area.
A ski jacket is a must. Choose one that has a zip-in liner that you can take out on warm days or add in for cold times on the slopes. Many ski jackets have pit zippers under the arms for extra ventilation when you need it; this is a nice feature to have.
Don't forget gloves. Go with waterproof ski-specific gloves or mittens. Some models come with liners that can be taken in or out, and worn by themselves on warm days.
Helmet and Eyewear
Even if you don't plan to hit anything, a helmet is a great idea. It will protect you from collisions with other skiers, as well as from hitting your head on hard-packed snow or ice when you fall.
Finally, protect your eyes from the cold and sun with goggles. A decent pair isn't a big investment, and you'll be much more comfortable when you're heading down the slopes.