I wear bifocals (not progressives, though). I have a pair for regular use (driving, watching TV, etc.). But I have a different pair of bifocals for when using my non-DAW computer and a different pair for using my DAW computer which has a larger screen further away than my non-DAW screen. Fortunately, my older non-DAW glasses became right for my DAW as my eyesight slightly deteriorated. I can't imagine not having computer-specific glasses - the requirements are very different from those when the upper part of the lens is for the longer distances of everyday non-computer activities.
Next time you see your optometrist, go in with measurements of how far your computer screen is - it is probably a bit further than the distance for reading a book. You might be very well served with a computer-specific pair. I'm perfectly happy with bifocals and don't feel any need for progressive lenses for my computer glasses, which probably saves a significant chunk of change.