As a beginner you will be able to hire the expensive bits initially and always take advice before splashing out on your own gear.
Snowboards are made to fit different sizes and weights and abilities, so getting good advice is vital.
Alpine boots are hard and freestyle boots (the most popular kind) are soft. The softness gives you the freedom to perform lots of tricks, and makes for easy carving on just about any slope.
You will need a good ski jacket, trousers or salopettes (dungaree-style trousers). All will need a weatherproof outer layer and you can choose between insulated or non-insulated varieties.
Get some proper sunglasses to protect your eyes with full UV protection.
A well fitting hat will be required to protect you from the cold mountain air.
Wear gloves to keep your hands warm and dry and provide protection on Snow on artificial surfaces.
When you first try the sport it is best to rent the equipment. Once you're hooked it's great to own your own kit. Modern snowboards are designed to make learning and progress a snap, so good advice is worth a lot.