The single most important personal item in the field will be your canteen.  Dehydration is an ever-present threat during the hot summer reenactment season, and keeping well- hydrated during drill or battle is of high importance.  Always make sure your canteen is full when mustering for drill or battle.

Civil War canteens were typically tin, with two halves soldered together and a tin or pewter spout with a cork stopper.  Wooden versions were also quite common, particularly in the south.  Today, many reenactors prefer a stainless steel canteen, which, while technically "farby" will tend to outlast a tin canteen many times over and if covered with a wool cover, will scarcely be noticed as stainless.  A wool cover, soaked with water, will keep your canteen much cooler due to evaporation. Coating the inside of a tin canteen with beeswax will greatly extend it's life.  Never put anything but clear water in your canteen, and store it empty with the stopper out between events so little critters don't start growing in it.

As a mounted cavalryman, you have your choice between a "mounted" canteen strap (which attaches to the saddle) or a shoulder strap style which is worn across the body from right shoulder to left hip.  Most infantry canteens have a rather long one-piece strap of either cotton or linen which is then adjusted by tying a knot to raise it to the proper height.  Straps wear out long before the canteens and covers, and some prefer to make a leather strap which was also period correct.

Take your time selecting your first canteen, for it's going to be your close companion for a long time.  In surfing through online sutlers, you'll find many styles such as flatside drum,  "bull's-eye", etc.  Remember as a Confederate you can carry captured Yankee gear, so in reality any CW period canteen can be "correct" for your impression.  A disassembled canteen half was often used as a mess plate.

However, it's best to avoid the earlier, "kidney shaped" revolutionary war style or the later, "Indian War" period styles, shown below. 

"mounted style strap" on a wooden canteen.

common Confederate style tin drum canteen

Stainless Steel drum canteen with gray wool cover
(not a bad first choice for a new recruit)

The saber, or sword belt is a pretty complex rig.  For starters, it's a sturdy belt which must support your pistols, cartridge box, cap box, and saber if you wear one.

The shoulder strap provides extra support for the left side, where the saber is worn.  Two longer leather straps of different lengths hold the saber down low to the side and at a proper angle when mounted, and a small brass hook holds the saber up snugly to the side when dismounted.  

Here's another piece of leather gear that's going to get a lot of use.   This holds your caps for your carbine, and secures with a Sam Browne button ( again, never a snap ).  Make sure it has a small piece of fur sewn into the top along the top edge - which was standard, and prevents caps from spilling out.  The model shown was a very common Confederate cap pouch, but many other variations are widely available.

This holds your cartridges, and usually is worn on the right-side rear of the sword belt.  Some mounted troops prefer to wear it on the carbine sling up front.

Be careful you don't get the larger infantry cartridge box - this is incorrect for mounted cavalry.