What you are talking about is a sieg 7x14 lathe, sieg are the company that make them in china, although they are sold under dozens of brands. http://www.siegind.com/
You should be able to find a fair few existing conversions in the project logs section of this forum.
I dont have the same lathe, so i cant really comment on the hardware, but here is a rough list of the electronics requirements.
There are literally hundreds of options, but assuming you have a budget, this would be a reasonable place to start:
Two popular approaches:
Build a linear power supply
Cobble together a load of cheap PC psu's
The linear one would be the better option, but the pc psu approach is very cheap, more efficient power usage wise. Personally i have built linear psus for my mill and lathe, they are pretty easy to hook up, and there are countless guides on the forum on how to do so.
servos / encoders
Ebay is your friend for sourcing these, you regularly see servos going for cents on the dollar. You are looking for brushed DC servos, with encoders included. You can get encoders seperately, but its a pain to fit them, and usually you can get motor+encoder on ebay for less than the encoder costs new.
servo drives with step direction inputs
You will have trouble sourcing these second hand, as industrial drives tend to use analog or pwm control signals. There are quite a few different hobbyist targetted brands around, and geckodrive seem to get a good reviewm although i havent used them myself http://www.geckodrive.com/product.cfm?pid=14
breakout board / pc interface
This is what hooks the servo drives to the PC, a good quality opto-isolated parallel port breakout should be all you need. I got mine from www.cnc4pc.com.
Spindle speed measurement
Basically you use a beam break sensor to read index pulses from the spindle, so you can drive the servos with electronic gearing for screwcutting. I have one from cnc4pc above that includes everything you need.
Something thats reasonable with a printer port, ideally dedicated to being the lathes pc, you will probably have to strip down a copy of XP, so its best that its dedicated. Laptops are ok, but some have out of spec printer ports on them, so its something to watch out for.
Mach is a good choice, its pretty cheap, windows based, and has a massive amount of community support (see the forum section here).
EMC2 would also be good, its based in linux (but does come with a bootcd release), has community support, and is free software.