Instructions
Talk to your dungeon master about equipment. Ask how much gold you will be given to start with. Also ask if you should pick out equipment from the player's handbook, or if you must wait and go shopping once the game begins. See if you will be using encumbrance rules, which govern how much a character can carry. These rules can get complicated, and not everyone feels that they add much to the game, so some campaigns don't use them.
Check out your armor and weapon options. For most characters, these are some of your most important purchases. As a beginning character, you will probably have very limited purchasing power, but you should try to buy some sort of weapon and some sort of armor. The best weapon is the one you have proficiency with (or in some cases the one you are allowed--some types of character, such as mages, may have strict limits on types of weapons and armor, and are often limited to something small like a dagger).
Stock up on basic supplies. Buy some torches, flint and tinder (to light the torch), some food, a warm cloak and a bag to keep your stuff in. Some dungeon masters may not be sticklers for items like these, but they sure come in handy if you need them.
Choose some luxuries if you have lots of money left over. Especially for fighters, it can be very useful to have a bow or other long-range weapon and also a secondary melee weapon such as a dagger in case something happens to your main weapon. Also, a horse is very convenient for traveling long distances, though not if other members of your party have to go at walking speed.
Save some money if possible. It's important to buy a basic inventory, but you never know when you will need to stop at a restaurant, an inn or a specialized shop of some type.