Machine style torches will have no finger trigger and are designed to be triggered internally at the power source by the cnc controller. Machine torches are easy to mount rigidly to the lifter and are very easy to check for square due to the long vertical body. Hand held torch's will have a finger trigger which may need to be modified to allow your cnc controller to fire the plasma, have bodies of various shapes, angles, and sizes and as a result are more difficult to rigidly mount and square up. If you have the option to switch to a machine torch it is always recommended and not necessarily a waste of a perfectly good have torch since the hand torch can still be plugged in and used for hand help cutting when needed which is a very handy option.
When it comes to squaring your torch it will need to be checked for square on both the X and Y axis and depending on your torch lifter you may have hardware to adjust it or you may have to shim the mount. Check with your table manufacturer for best method if you find your torch is out of square. The machine style torch mounts I have seen are typically all very solid, but the hand torch mounts on the other hand could use some work the make them stronger. I believe the reason they are typically flimsy is due the fact that they are designed to mount all torches of varying shapes, angles, and sizes and need to be universal. If you are decided on the hand torch you will be cutting with you can use some ingenuity to modify the mount to be more rigid for your particular setup. See the Hypertherm® machine and hand torches from the Hypertherm® manual shown below.
Be sure your torch is rigidly mounted to eliminate vibration, and be sure to square the torch on both the X and Y axis. If your torch is square and your seeing a tapered edge on your cut do not be tempted to correct it by angling your torch to compensate. Your problem lies somewhere else and is likely due to worn consumables, incorrect direction of travel, or incorrect cut height.
Good luck and have fun
