If you want the ramp to be monotonic (constantly increasing), your resistors will need to be matched to around 0.5%. The absolute value isn't particularly important, but the matching is.
If not for the fact that you would need a current limiting resistor for each LED, I think the easiest solution is a shift register made up of 74HC164's. You get 8 bits per package, so it would take 13 of them to get 100 outputs, but you wouldn't need a ramp generator or the LM3914's. The advantages of the 3914 are built-in current limiting, and 10 outputs per package vs 8 for the HC164.