Servo's V steppers.
But after you have read this you will be no better off as there are many conflicting setups.
[1] Main difference between servo's and steppers is that servo's are equipped with an encoder so they know at any point where they are. [ more later ]
[2] Steppers are usually direct drive unless you need a reduction to get more power like on a Z axis as steppers have most power at low speed. Servo's OTOH need loads of reduction gearing as they run far faster which is where all their power is.
Main rule of thumb is steppers are OK on small machines, servo's are needed on large machines.
Now for the more later.
True industrial servo systems have the encoder feed back going to the controller so it knows where it is and if it isn't, can do something about it. Hobby servo's because they use controllers like Mach 3 that cannot take an encoder feed back into the controller rely on the feedback going into the driver.
Now the driver will do it's utmost to make it go where it's told but the controller is blind to this. The industrial setup is a true closed loop, the hobby setup is a quasi closed loop.
Now to throw even more into the pot you can now get three phase steppers with encoders, basically making then a servo system.
If you were confused to start with you will be more confused.
Long short on something like a SX2 or SX2P then stick to a well designed stepper system as it will do more than you and the machine are capable off. 3 axis servo's will probably cost, on their own twice what the machine costs and will not do anything any better given the donor machine.
Personally I'd go the ball screw route from the get go. You need one screw anyway because the Z is on a rack and pinion.
DO NOT ATTEMPT to motorise this, the errors are far to great and if you do I'll have you banned from this forum

You can get three ballscrews, with nuts from China for about £120 UKP don't know what that is in $OZ
3 steppers 270 to 350 oz/in
3 M542 drivers
Power supply rated at about 40v DC
Breakout board plenty of USB ones out there now from China so no worries about a computer. DO NOT USE A LAPTOP.
Hand full of shiny bits and you are done.
End of the day you will have a workable machine, not the best out there but also far from being the worst.