Though this discussion is quite basic, many of the attendees in my CNC seminars are so surprised at this presentation, I assume that many people have not considered the implications of this question.
Almost all current model slant bed turning centers allow machinists to use either right- or left-hand tooling. With some machines, the hold-down bolts are placed in different holes. On others, the cam-lock system is inverted. But by one means or another, each turret station can be made to hold tools of either type.
If holding tools designed to machine in a direction toward the workholding device (Z minus), right-hand tools require an M03 (spindle forward) direction, and left-hand tools require an M04 (spindle reverse) direction. Since most cutting tools are more readily available in right-hand versions (right-hand tools are commonly less expensive and are purchased off the shelf), and because some operations must be performed with right-hand tools (tapping and right-hand threading, for example), most CNC users prefer using right-hand tools. Many shops use them exclusively.
Keep in mind, however, that your turning center's rigidity and strength will commonly be better with left-hand-tooling. The drawing here shows why. Notice that when left-hand tools are used, the force of the machining operation is thrown into the machine's bed and machining will be very stable. On the other hand, notice that when right-hand tools are used, the force of the machining operation tends to pull the turret away from the machine bed, and machining is less stable.
For light duty machining, it truly doesn't matter which type of tooling you use. But as machining operations become more powerful (as is the case when performing heavy rough turning and boring operations), left-hand tools are better. You would be best off using them and sacrificing the cycle time it takes for spindle reversals. And by the way, if you experience problems with inconsistent sizing (even for finishing operations) on tight tolerances, using left-hand tools will improve the stability of machining.