How many Stones does it take to go all the way

world-of-warcraft

Just for the sake of completeness, I'm going to take Chris' profession guide link and reduce it to ore amounts. That'll at least give you the "minimum" amount.

Absolute Minimum

The technical absolute minimum is 0 ore, as you'd just buy all the bars/gems you need from the auction house and you'd never deal with ore at all.

Minimim w/ Mining

This answer will include the minimum figured assuming you only mine for bars and dust and that all gems come from the auction house.

160 Copper Ore
60 Tin Ore
140 Mithril Ore
15 Truesilver Ore
50 Thorium Bar
200 Adamantite Ore
10 Titanium Ore

Minimum w/ Mining & Prospecting

This answer assumes that you'd obtain each gem from the common ore most likely to drop it via prospecting based on figures on Wowhead. However, I also assumed no gems dropped during mining, which means these values won't be the absolute minimum.

160 Copper Ore
310 Tin Ore
- add 150 more for Horde characters
- add 200 more if you'd rather not farm/buy Small Illustrious Pearls
125 Iron Ore
215 Mithril Ore
15 Truesilver Ore
250 Thorium Ore
- add 50 more if you'd rather not farm/buy Powerful Mojos
200 Fel Iron Ore or Adamantite Ore
- add 75 more if you'd rather not farm/buy Black Diamonds
220 Adamantite Ore
350 Cobalt Ore
25 Saronite Ore
10 Titanium Ore
3205 Obsidium Ore (500 + 2700 from Shadowspirit Diamond and Fire Prism transmutes)

Quick Average: Mining & Prospecting

For the purposes of this answer, I assume that everything you do will skill you a point in Jewelcrafting, but I incorporate the average percentage drop of gems from the ore that is most likely to drop that gem.

For obsidium ore, the figure is the same as the minimum. Assuming each gem has an equal chance to drop, you'll be obtaining the gems in equal numbers. Since you need 3 of each of them for the transmutes, the percentage that you'll get a gem you need is 100% until you've gotten enough of that gem for all the transmutes you'd need.

160 Copper Ore
755 Tin Ore
- add 400 more for Horde characters
- add 535 more if you'd rather not farm/buy Small Illustrious Pearls
420 Iron Ore
390 Mithril Ore
15 Truesilver Ore
1155 Thorium Ore
- add 170 more if you'd rather not farm/buy Powerful Mojos
1180 Fel Iron Ore or Adamantite Ore
- add 445 more if you'd rather not farm/buy Black Diamonds
310 Adamantite Ore
1400 Cobalt Ore
140 Saronite Ore
10 Titanium Ore
3205 Obsidium Ore (500 + 2700 from Shadowspirit Diamond and Fire Prism transmutes)

Quick 90th Percentile

With the absence of data points from actual instances or simulations, I cheated on this one. My calculation for the 90th percentile was (([AVG]-[MIN])+[AVG]*.9)+[BAR], where

AVG - Average ore needed to prospect gems based on drop rate
MIN - Minimum ore needed to prospect gems
BAR - Ore needed for bars

It's not perfect, and it also assumes that you always skill when crafting things with jewelcrafting. The same caveat applies to Obsidium in this answer as it does in the quick average.

160 Copper Ore
1120 Tin Ore
- add 610 more for Horde characters
- add 815 more if you'd rather not farm/buy Small Illustrious Pearls
670 Iron Ore
540 Mithril Ore
15 Truesilver Ore
1950 Thorium Ore
- add 550 more if you'd rather not farm/buy Powerful Mojos
2245 Fel Iron Ore or Adamantite Ore
- add 765 more if you'd rather not farm/buy Black Diamonds
385 Adamantite Ore
2310 Cobalt Ore
240 Saronite Ore
10 Titanium Ore
3205 Obsidium Ore (500 + 2700 from Shadowspirit Diamond and Fire Prism transmutes)

True Average & 90th Percentile

It quickly gets too complicated for me to want to bother attempting this in a completely legitimate fashion. One would have to make sure they had enough base inventory to accomplish both feats which results in a trickle-back effect where you have to go back and make older stuff again at times. That's best left for either a simulation program or someone with free time and a burning desire to snag your bounty. :)

For anyone interested in doing that, good luck. Also, so it doesn't get missed, Raven Dreamer posted the skill up formula he found for the percent chance you will skill up on a yellow or green recipe as a comment to the original question:

[chance of gaining skill point] = (grey skill - current skill) / (grey skill - yellow skill)

"Grey skill" and "yellow skill" are the numbers at which the recipe turns grey or yellow respectively.

This isn't an answer by your criteria but this guide contains the materials required to level to 525, some people may find it useful: http://www.wow-professions.com/wowguides/wow_jewelcrafting_leveling_guide.html