From what i understand these are fien machines.
The question here is the condition of the original controller and programming.
There seems to be a debate and often differing opinions on how much of the original contrals can and should be kept in tact. Some prefer the vintage original controls other wish to modernize the controls and run from a pc or laptop.
To run completely from a lap top you will need a control program say mach 3 .
$175 and a smooth stepper motion cotroller eithernet version IIRC $200 and a controller G540 $299 and a power supply about $50.
So to run from a modern lap top you pretty much need to bypass the original controls.
It may be possible to write g code on a laptop and transfer to the original controller. via a cable do not know.
Tin
you often dont need external hardware with linuxcnc like you do with mach. depends on the motherboard. also there are many motherboards that are in the $80 range with built in cpu like the atom series and amd apu that can run on a low power, inexpensive pico psu, have ample power and have built in parallel ports or headers. the g540 is a great option. i agree with that. but you can also build up some linisteppers from kits on a machine that small. the hal on linux cnc might take a bit to figure out but you don't need to be linux fluent. linux installs easier than windows and the gui is strait forward, it's not linux that makes linux cnc difficult! you don't need to know shell commands or navigate the file tree structure to set it up. the hal is a part of linux cnc and you will need to do a lot of reading for that. you may be able to find a hal for the stock stepper drivers, or a common stepper driver such as a g540 though....
laptops are not linux cnc friendly... there is an alernative... it costs $80 (you still still may need a gecko drive or a couple linisteppers if the existing drives are weird.) it runs on any of the popular OS's, windows, linux,, mac, bsd, whatever... it's called RTstepper. and it's the path i'd recommend for a beginner that wants a SIMPLE modern control but it wont control the tool changer as far as i know. RTstepper is just the most basic features and is derived from linux cnc but replaces the complicated but flexible bits that make it so adaptable with a simple pre setup hardware device that works over usb and outputs parllel. it's literally the easiest way to modernize the machine, but you wont find as much support as for mach. it's not nearly as popular.
as far as using the stock computer but losing the tape drive and feeding it with a laptop... well if it's a standard parallel or serial port you may be able to do that. i'm not that savy on old computers but i seem to remember there being a way to print out text files as the recieving computer needs them. i don't know if the lathe has internal memory that the program gets uploaded to in advance or if it reads small sections of tape as things run but either way it should be "possible" if you get some pictures of the port and any info on the communication protocol.. this might be doable through some simple command prompt on a windows machine (just like running DOS) as well as anything that runs a terminal shell (linux, mac, bsd)
linistepper (cheap and QUIET and not as fragile as things from china)
http://www.piclist.com/techref/io/stepper/linistep/LiniV2_bld.htm
more pricey but totally worth it as they are indestructable
http://www.geckodrive.com/geckodrive-step-motor-drives/g540.html
rt stepper (easy!!! and cheap, runs on any existing computer you may have laying around, even a raspberry pi!)
http://www.ecklersoft.com/
linux cnc (harder but completely free)
http://www.linuxcnc.org/
edit: i just want to emphisize you don't need linux fluentcy for linux cnc, but you need to learn about the software itself. it's not entirely plug and play but it looks like there is a good link above on this. i don't know if rtstepper or mach can do the 4-phase drive, so they will obviously be a bigger investment, but i think it would be easy to program an arduino or pic of some kind to convert quadrature or step/direction over to 4 phase which could save some money over a drive replacement.