Appropriate Computer: First of all, you are going to need a decent computer. This doesn't mean you go to the store and purchase the first computer you see, or the most expensive computer. Usually these will have to be custom built machines. If you are technically inclined then you will be able to build your own machine, though there are designers out there who are unable to do this and will need to outsource the work to someone else.
One particular machine that has been noted for its design capabilities is the Macintosh or Apple PC. These are machines centered around graphic design and based on a variant of the UNIX operating system. These machines are usually extremely powerful, having more processing capabilities than a standard personal computer. Though that's not to say design cannot be achieved on a standard machine. In fact, there are many out there in graphic design jobs that use a standard Windows PC every day. It's really a matter of personal preference, but it is still incredibly important to make sure that one gets the right hardware.
Design jobs are going to require some peripherals for the computer, some of which depend on the computer, some of which do not. One of the most important tools you can get for design jobs is an external hard drive. This will help you to store your work off of your main hard drive, which leaves room for two possibilities. First of all you can transport it easily, and secondly you will still have all of your work if your main hard drive happens to fail.
Software: There is too much to say regarding this topic, but we'll try. You are going to need a stable operating system for design jobs, and on top of that you are going to need some software to make your graphic design work possible. There are many software suites out there for editing photos and images, some of them free, some of them less so, but either way you'll need to figure out what you want to use.
These are a few of the tools that anyone in design careers is going to need. There are quite a few more, but you will likely come across these sooner or later when the need for them arises. Keep your eyes open for new software that will help further you design career, because you never know just what might come up! New software is being made everyday, and the same goes for equipment. Always make sure you are adequately prepared for this type of job. After all, it's going to surprise you every day!