I will start with the most obvious piece of gym kit simply because I have seen too many gym goers carrying all their kit in their arms. A gym bag is all you need to store all your gym kit in. They come in various shapes and sizes but I prefer the duffel bag style or the newer barrel bag style to anything else. Try and choose one that has separate compartments within. That way you can store any coins, car keys or mobile phone without losing it amongst your other gym kit.
Some people prefer not to carry one of these around in the gym but a water bottle is a must. Keeping hydrated when working out is one of the most important factors when fighting fatigue. Take a look at my article on protein shakers, which also make great water bottles. Be considerate to others using the equipment by making sure you have a small towel with you. Wipe down the handles of the equipment you use so it's clean for the next person. Obviously you can also use the towel to dab the sweat from your body!
Next up, you'll want to make sure you stay motivated through the hardest parts of your workout. One of the best, proven ways is to take your favourite music with you. Whether it be on an iPod or an MP3 player - make sure it is in your gym kit bag (and fully charged).
Support and injury prevention
If you're thinking of starting lifting weights, you should consider getting weightlifting gloves and some straps in your gym kit. The gloves will help prevent blisters forming on your hands, and the straps will help you lift more weight (because your grip won't fail as quick). While we are on the subject, a weight training belt is also essential to preventing injury so add that to your gym kit too!
The final thing I think is essential is a gym sack, these are cheap draw-cord bags to store your sweaty clothes in after a workout - you'll want to keep them separate from your clean gym kit.