When you go shopping for horse gear, try to buy the best that suits your needs and pocketbook. Well made leather, silver, bits, spurs, rawhide, blankets, etc. will give good service and last a long time if taken care of. In fact, some items such as saddles, bits and spurs, can actually go up in resale value. If made properly, they can aid in your horsemanship and the performance of your horse rather than detract from your experience and work.
There is a large variation in the gear needed depending upon the type and style of riding you do. This is just an overall list to start.
Headstalls for both snaffles and shanked bits that fit and are adjustable.
A variety of snaffles with snaffle hobbles
Split leather reins or CC's weighted Pro-Trainers with poppers or
Slobber straps and 5/8ths or 1/2 inch mecate
Hackamore/bosal---to start, usually 5/8ths inch, but can be 3/4 or 1 inch then 1/2 inch, then 3/8 inch and, finally 1/4 inch for the finished horse (can be employed by a latigo hanger under the headstall or via a single string on the front of the face attached to the forelock
Mecates---a series each within a 1/4 inch diameter of the rawhide, leather or kangaroo bars
Get down rope---usually 16 foot and 3/8th inch diameter of mane, angora or nylon with a popper on one end and a small lash on the other end. It can be tied around the horse's neck in a bowline (a knot that will not pull down tight) or dropped down nearer the chest and then brought up when needed). These are not for tying a horse, but for leading---especially a horse in the bridle. Ernie Morris says, "Don't leave home without one".
A selection of shanked bits with a variety of mouthpiece options
An elevator bit
Leather curb straps
Romal reins made of rawhide, kangaroo or calf
A good fitting saddle for both horse and rider that is appropriate for the job
A cinch that is made of natural materials that allows air circulation and is the corrrect length
Appropriate and clean pads and blankets that allow the air to circulate and the horse's back to "breathe"
A good rope halter with a 12-16 foot lead