Eye Protection: This is the most important piece of equipment, and it is often neglected. I see it all the time too on the Internet of people shooting without eye protection, I have even been guilty of it from times past. But I will not be caught out shooting without it. Eye protection saved me one time years ago, it wasn't even really eye protection as much as it was me keeping my sunglasses on. Someone I know made an exploding target, and we were out in the desert shooting and when the target hit and exploded it sent a piece of gravel right right at my face and actually hit the bottom of the frame of my sunglasses barely missing the side of my face and hit my earlobe as it went past. Now I know shooting exploding targets isn't the most responsible thing in the world to do, however if that gravel hit me or someone else in the eye it could have taken an eye out.
Just yesterday I was at my local range shooting on some steel bobbers (steel pop up targets) and a piece of copper jacket (aka splatter) from the bullet hit the steel target and caught me in the leg and embedded in my shin. Splatter is super hot and it hit me with some serious force. This type of incident isn't uncommon and if you get hit in the naked eye with a hot piece of copper jacket at and incredilbe speed your eye is gone. So go and buy some shooting glasses. I bought mine at Wal-Mart for around $6, and I will not shoot without them.
The other piece of essential equipment is hearing protection. There are many types of hearing protection, but for new shooters keep it simple with ear muffs or foam ear plugs. You can get a set of ear plugs for $.30 some places so there is no excuse for not buying some. Every couple years I will buy a box of the orange foam ear pugs and keep some in my range bag and also in my vehicle. Someone will always forget hearing protection, and that someone includes you. The ear muffs I have currently I purchased at Harbor Feeight tools on sale for $3.00 and I like them more than some of the $15 dollar models I have also owned,
I remember the first time I shot a hand gun I was probably 6-7 years old. It was my dad's .22 revolver, which he still owns, it has a dark blued frame with pearl looking handles. He also had this tan leather holster that looked like something a cowboy would keep that very gun in, and I loved cowboy and western movies. I even had a coon skin cap ( a fake one I get at Disney Land) due to a recent obsession I had with Davey Crocket at the time. So I took this cowboy looking gun and pointed it out across the barren southern Nevada desert like I had pictured Davey Crocket doing, cocked it, and pulled the trigger. After this amazing experience I experienced something that I had never experienced before that was as equally frightening as shooting like a cowboy was exciting; a ringing in my ears. I had never experienced this sensation in my 6-7 years of life and I thought I was going deaf and would have to learn sign language like Linda the deaf lady on Seasame Street. To my relief I still have my hearing which appears to still be pretty good to everyone except my wife.
This experience prompted me to attempt to use hearing protection starting at a very young age. Working in this industry I have many friends who didn't use hearing protection that often when they would shoot and have sustained permanent hearing loss.
Where you are starting out invest in some hearing protection and eye protection early on; make it a habit.