The first and most important piece of safety equipment is your eye protection, (eye pro). An airsoft BB can easily cause a serious eye injury so this is the most important piece of equipment to keep you safe when you play.
Whatever goggles you choose should be made for airsoft, or paintball. Avoid using shop goggles or safety glasses from your local hardware store. They may have the proper impact ratings but they aren’t intended for this sport. Your eyes can’t be replaced, invest in protecting them.
The second thing you should look for is that your eye pro should be full seal. This means that they form a complete seal around your eyes that will keep a BB out. Good goggles will do this if you wear them correctly. Goggles like the Valken V-Tac Sierra are a good way to go.
The second piece of safety equipment you need to have is face protection, (face pro). The main concern with face pro is that it will protect your teeth from being hit directly by a BB. An airsoft BB can knock teeth out or crack them and that is expensive to fix. Different types of face pro will provide different levels of protection. Some like the Valken 2G Wire Mesh Tactical Mask provide protection to the front of your face, primarily over your mouth nose and cheeks. Others like the Valken 4G Wire Mesh Tactical Mask provide protection to your ears and to more of your face. Either is totally acceptable for airsoft.
There is another option which combines eye pro and face pro into one package. That is to buy a set of paintball goggles, like the Valken Identity. These systems give you a very high level of protection. For Speedsofters paintball goggles seem to be the system of choice. Milsim, (military simulation) players tend to stay away from them. So the type of airsoft you are going to play may influence whether you want to use paintball goggles or not.
Once you have eye pro and face pro you have the basic equipment you need to keep you safe in this sport. Depending on your level of comfort with getting hit you may want to add more protective equipment and of course there is more you can get.
Valken makes a line of helmets specifically for airsoft. Being hit in the head can sting quite a lot and in some cases leave a pretty good lump, so helmets are a popular addition to many players equipment. For indoor play they also add an extra bit of protection against bumps. As well many of them allow you to mount action cameras, lights and in some cases your goggles directly on them.
Ear protection is an often overlooked option, and probably the most painful hit I've ever taken was a shot to my ear. There are couple of options here. One is to use a product like the Valken Tactical 3G Wire Mesh Ear Protectors These are designed to work with a helmet and they are a lightweight inexpensive option to protect your ears from impact.
Another option is to go with a set of electronic hearing protection . This type of equipment will not only protect your ears from physical impact, but they will also reduce loud noises that could damage your hearing while amplifying quiet sounds. If you are playing in an environment where distraction devices like the Thunder V are being used this can be a very good option.
A plate carrier can help reduce the sting of hits to your body as well as providing a place to mount pouches to carry spare magazines and other supplies. This is a pretty essential piece of gear that almost every player uses.
Gloves are a good option as well. Getting hit in the hands really sting and you will find that as you learn to play and use cover properly getting hit in the hands will become more common because that's all that will be exposed.
Schemaghs are useful to protect the exposed skin of your neck. Some players use these to protect their teeth as well.
There are all kinds of equipment available to take the sting out of airsoft, as well as to protect players from injury. The key is to buy quality gear that works for you, over time as you gain more experience playing you will refine your equipment choices as you find what works best for you.