Jackets come in different types; shell and padded.
Shell jackets are the non-padded thin jackets that function as windbreaker and keep heat inside but expel moisture from your body. They are great for riders in warmer climates. These are easier for layering in case you get too hot.
Padded jackets are thicker jackets that have insulation. They are great for riders in colder climates as they keep you warmer. Padded jackets would be a good idea if you spend a lot of time sitting on a chairlift (gets pretty damn cold on those, esp on windy days)
Before buying a jacket, you need to consider waterproofing and breath-ability of the shell.
The higher the number is, the better it is at staying dry and expelling moisture. 5,000 is the usual waterproof and breath-ability number on the lower-end jackets. If you want a decent jacket, go for anything higher than 15,000 for waterproof and 10,000 for breathability.
Gore-tex material is the top-end stuff you can get on most outdoorsy tech gear, but they are quite expensive.
When you get a new jacket, try it on, play with it and inspect every inch of it. You may just find hidden pockets and sometimes goggle cleaners on a string hidden away in a pocket. Its like a treasure hunt.
Because snowboarders and especially beginner snowboarders tend to spend much more time on their butts than our counterparts on 2 planks, pants with extra padding on the butt area is very much preferred for snowboarders.
You might want to check out the practicality of the pants, like the number of pockets, waterproofness of the zips, its compatibility with belts and the pants version of pit-zips on the insides of the legs (esp. important for backcountry boarders who hike a lot)
Try them on before purchase, make sure you can squat in them comfortably- this makes sure that you wont be restrained by the tightness in your pants while riding.
Snow skirts usually come with jackets and most are removable with a zip. Some brands make snow skirts with pants as well, but in my opinion snow skirts on jackets are more comfy and easier to use. They are meant to cover the top of your pants with tight elastic to prevent the snow from getting shoved into your pants.
Gloves- get nice, thick and toasty gloves made specifically for snow sports. They are waterproof, thickly padded and are relatively good at expelling the sweaty moisture from your hands to prevent the inside of the gloves getting waterlogged (ugh). They also have rubbery material on palms for good grip and drawstrings on wrists to prevent snow from getting in.
If you are a beginner and is planning to use wrist guards, make sure you get gloves that provide you with enough space for the guards.