Here are some necessities for playing softball. The coach usually supplies batting helmets, catcher’s gear, and first-aid kits but there are some other things players may find helpful.
When playing the field, infielders wear a facemask or a fielder's mask to protect their face from a ball hit at close range. It is like a catcher's mask but is lightweight and enables the fielder to move around easier when wearing it.
Mouth guards protect a player's teeth and tongue against damage in many situations. There are many varieties available. Just find one that you are comfortable wearing.
Hats are useful for keeping the sun or hair out of one's eyes, especially if it is very sunny or windy. A hat is also helpful to someone who wears glasses when there is a slight rain. Sunglasses may be an alternative to wearing a hat but do not keep out as much sun.
Sliding shorts are very helpful if you need to slide. They are lightweight and can be worn underneath a uniform. The padding on the sides or back helps cushion sensitive skin against abrasion when sliding. The shorts protect upper leg areas but there are protective pads for almost any body part you can think of. Men can wear athletic support shorts with a cup. Catchers can wear thumb protectors, pitchers have shirts to protect the chest and back, and arm guards for their pitching arm and batters can wear an elbow pad to protect themselves from the ball.
Batting gloves have many uses for softball players. When a batter wears them to hit, some of the shock of contact by the ball is absorbed through the gloves. Gloves are also good when gripping the bat so it does not slide in your hands. Many fielders wear their batting gloves underneath their fielding gloves for a better fit and runners wear them when sliding to protect the their hands from injury.
A good pair of cleats can give a player more traction when running and an edge when you need speed. The cleats dig into the dirt when running and keep you from slipping if you are running on grass. This is a huge help to outfielders when they are chasing a ball and have to stop suddenly. If the grass is wet, it is almost impossible to keep your footing without cleats.
These are just a few items that can protect your body or improve your game so they are not mandatory for playing your best. Everyone has their own preference so some of these may not interest you, but for protection, the gear that safeguards against injury should be worn.