While it's unlikely that the average rider will have a serious accident nearly all riders eventually do go down at some speed if they ride for any significant period of time. Being prepared for a potential crash with the right protective gear can often mean the difference between getting up and walking away and a visit to the emergency room. The law in most countries typically requires that the rider wear some basic gear to operate the motorcycle any time they are on a public road. While the law of course varies from place to place, most require a helmet and gloves at an absolute minimum. It is of course wise to go beyond these requirements if you value the condition your body.
Head: I personally recommend a full-face helmet for safety reasons, but many prefer the feel of open-faced helmets with no visors. If you decide to go this route, be sure to wear some protective glasses or goggles to keep debris out of your eyes. Better hope you're lucky and that nothing bigger comes at your face at 60mph. As someone who has hit a bird with their full-face helmet at this speed, I can tell you from experience that it's not going to feel good. Make sure your helmet fits snugly, and always keep it strapped up firmly. A loose or unsecured helmet is going to fly right off on a serious impact.
Hands: Gloves are a crucial part of any rider's gear. If you go down on your bike your first instinct is going to be to put your hands out to brace yourself for impact. Asphalt is going to chew through skin if you don't have some good protection here. Both leather and heavy duty textiles are commonly used to produce motorcycle gloves. Which is better? Tests have shown that even the strongest nylon cordura grinds away well before standard-thickness leather does, but continuing research on new and existing materials is helping to bridge this gap somewhat. Since the hands contain many delicate bones, going with a pair that offers some sort of impact protection in the knuckles or elsewhere is a good idea. In cold weather make sure you wear gloves that keep your hands warm. Cold hands can't move as quickly, and you always need to be able to react at a moment's notice.
Jacket and Pants: Again, the same rules apply. For the best abrasion resistance leather has the clear advantage over textiles. Textiles do have the benefits of being lighter and more comfortable than leather, so it really comes down to personal preference here. Whatever material you decide to go with, make sure that is has (typically CE) approved armor in all the important places. Shoulders and elbows are especially vulnerable, but if you can afford it choose something with some chest and back protection as well. There are some really great spine protection solutions that are comfortable and quite non-invasive. Function is more important than form here so get something that will serve you practically first and foremost.
Boots: Get something with a non-skid sole, oil resistant if possible. Regular old leather work boots will work fine here, though getting something purpose-built for motorcycling is always preferred. There are some initially subtle design differences in motorcycle footwear that make a very real difference during riding. For example, motorcycle boots are always lower-profile than a typical work boot to make getting your toe over and under the shift lever less cumbersome. Ankle protection against impact and twisting are important. Browsing boots you may notice that nearly all of them avoid using laces. This is also important design choice, though it's often overlooked. Hanging laces can be caught bits of your bike when you try to put your feet down which can lead to a really embarrassing drop at a stoplight. If you're going to wear something with laces make sure to tuck them in before every ride.