Here's a basic list of what you will need to become a sushi chef:
This is a rolling mat, often made of bamboo, and it will serve you to roll the maki. The makisu makes this work a lot easier, and it helps to keep your maki tight. If you want to do a "California roll", you will need some plastic paper so the rice stays well in place. Nowadays it's pretty easy to find, and it doesn't need to be fancy, a cheap one will do.
Using a metal spoon (or container) is really bad for sushi rice. It breaks the grains and if you want a perfect rice, you will need a wooden spoon. If you buy a sushi kit, they usually come with the makisu.
Nothing worse than ruin your beautiful maki by cutting it with an unsharpened knife! Make sure you've got a good blade. Today it's easy to find some inexpensives Japanese knives on the internet, and for a personal use, they will be enough. If you buy one of these you'll have to learn how to sharpen it well, but it's not so hard with a little practice (and it's very relaxing too !).
This traditional wood recipient is used to cool down the rice once it's cooked. His large round shape gives a good contact surface with the air, and the wood has good moisture absorption properties. As it isn't so easy to find, you can use a large plastic bowl as a recipient for your sushi rice.