I recommend going into a store to get a feel for a stick before buying. They range in size, 32" to 38" and are a personal preference.  Forwards tend to play with lighter sticks, as it aids stick speed during dribbling, whilst defenders often like a heavier stick as it will be more solid. Carbon content affects stick stiffness. Higher carbon sticks can often hit harder, however, they are less forgiving. A lower carbon stick (40-70%) is likely to provide a nicer experience while learning the basics of hitting/slapping.

Field hockey shin guards provide ankle-to-knee coverage because of the heavy sticks and balls involved in play. It is important to purchase shin guards made specifically for field hockey as they provide better protection than other varieties (i.e. Soccer). 

Refs can prevent you from playing if your shin guards are not ankle to below the knee.  I do not recommend soft shin guards, as the ball is very hard.

Get a good moouthguard, one that you can still talk through.  Many are now moldable to not just fit nicely, but allow for talking without the thing falling out.

These are generally the same goggles used in Lacrosse.  Note these are "cage" like goggles, not like glasses. Look to make sure they are Field Hockey ASTM 2713 certified.

Look to ensure that the goggles have the bar covering the eyes.  Not all lacrosse goggles have this should you have a pair of those lying around.

While goggles are no longer technically required, it is highly recommended to wear them.

The field hockey ball can be many different colors, but generally are white, yellow, or orange.  We play with official NFHS balls.

They are about 2.75" in diameter and weigh about 5.6 ounces.  They are hard.

Another piece of equipment which is not required, but is often worn, at least on the left hand.  It is the hand most likely to get hit by the ball or stick.  As it is the the hand on the top of the stick, it also touches the ground first and can lead to friction burns.

Of note, many girls do not use these, but for added protection, they are recommended.