I think that the concept of buying only three grits is fundamentally flawed. The starting point for your coarsest grit, is the finish that you get off your tool. There are experienced turners whose toolwork is good enough to be able to start working with 240 grit....ok, many of us achieve this very occasionally, but rarely, I guess. On the other hand, my experience tells me that many, many turners start with 120 grit.
The finishing point also varies. Many of us sand to 400 grit, following which I use 600 or 1000 Nyweb pads when I feel that they're needed, especially on dense woods like blackwood and yew, with which the finest of scratches from 400 grit often remain visible.
So, with there being variation between starting point and finishing point, it would be foolish to limit yourself to just 3 grits. Don't fall into the trap of believing that you can skip a grit, i.e. going from 120 straight to 240, it just doesn't work. What "Wooddust" has written is very valid.....there will not be a saving by limiting yourself to 3 grits, and it won't work anyway.
Les