I've never questioned my Starter Items and Core Items in my guides, but apparently some people do. No matter how I tried to explain why I prefer my way, all I get is comments like:

"Your argument is invalid."
"As a 1# guide on MobaFire you should teach people to play in the right way."

I get the sub-potential point, but this has been bugging me so I did some calculations on my own to prove my point why my way of starting with Rejuvenation Bead+ Faerie Charm+2x Sight Wards isn't any worse than the more popular 3x Sight Wards + 2 Vision Wards + Potions way.
People asked for proof/valid argument so I hope this answers for them. At least I spent hours doing this, so please at least appreciate the effort even if we have differing opinions.

I have to say I'm not a math genious, but I did my best. In case I did calculate something totally wrong, please let me know (and preferably do the math yourself if you don't trust me). I did it the most simply way, not including last hits, assists or kills, because that's something we can't predict. The gold starts running from the point it does in the game.

Gold facts:



In Summoner's Rift, the base gold is 16 gold/10 seconds. (http://leagueoflegends.wikia.com/wiki/Gold_per_10)

My guide gold income is 21 gold/10 seconds without Philosopher's Stone and from the point when you get it it's 26 gold/10 s. That means 156 gold in 60 seconds.
What people suggested me was to change the gold runes into HP runes and not buy Philosopher's Stone as a first item (or at all in some people's opinions). Their gold income would be 16+2 from Greed , which adds up to 18 gold/10 s.


Gold gain in 20 minutes:



Starting from the point when gold starts running:
  • Without anything (no masteries, no gold runes, no philo or any other gold item): 1920 gold
  • With masteries: 2160
  • With masteries and runes (no Philo): 2520 gold
  • With masteries and runes and Philosopher's Stone bought at 5 mins into the game (means stacking for 15 minutes): 2970 (means Philo gives 450 coins in 15 minutes)

2970-2160 = 810 gold difference in 20 minutes compared to having only gold masteries.


Gameplay:



Base gold with aupport is 525 gold (when using Wealth ). I assume people use Wealth and Greed masteries.

Starter Items:
Rejuvenation Bead+ Faerie Charm= 360 gold
+ 2x Sight Ward= 75 gold
= 510, you're left with 15 gold.


MY WAY 10 MIN BASE:



After being 5 minutes into the lane, I'm not saying you should go back, but if you're pushing and feel like it, why not? You don't lose much exp if your lane is pushing anyway, but if the enemy is pushing, you don't need to go anywhere, because you're relatively safe at turret anyway. I have left my carry alone to farm when it's safe and 90% of the time they don't go suicide.
After 5 mins, you have gained passively 630 gold + that 15 gold you had left from starter items. That equals as 645 gold.
Having started with Faerie Charm+ Rejuvenation Bead your core item Philosopher's Stone costs 340 gold.

5 min base:
5 min gold gain 630 + starting gold = 645
645 - 340 ( Philosopher's Stone) = 305
305 - 2x sight wards 150g + 125g Vision Ward
= 5 gold

10 min base:
Again, I'm not saying you should go back after being another 5 mins in the lane, but this is just for example and usually I do. Second time I do go back, I buy myself a Ruby Crystal, 2x Sight wards and a Vision Ward and this is how I calculated the gold.

Gold gain for 5 minutes with Philosopher's Stone: 2.6x60x5= 780,
- 475g Ruby Crystal = 305
- 2x75g Sight Wards
- 125g Vision Ward
= 30g (+ couple second wait and get a Mana Potion if you want)

From here on Sightstone will be ready after ~3 mins, which means you'll have it after 13 mins (after gold calculating starts) without lasthits, assists or kills unless you decide to buy boots first or more wards or die at lvl1 without achieving anything.
This is how I do it and how I recommend to do it, because often you'll have either assists, kills or last hits so you might even afford to buy Sightstone straight at this point.


SIGHTSTONE RUSH



This is the way I was suggested I should teach people in my guides to play. Without gold runes and without Philosopher's Stone rush (or not picking it up at all) and aiming for getting Sightstone as your first real item.

Starter Items:
3x sight wards
2x Vision Wards
2x Potions 35g each for your own choice.
= 0 gold.

OR

2x Sight Wards
2x Vision Wards
2x Health Potions
2x Mana Potions
= 0 gold.

Passive gold gain for playing like this 18 gold/10 seconds. Like before, no last hits, assists or kills are calculated into this. (Not even the Pickpocket mastery.)

5 min base
1.8x60x5 = 540

You get only 540 gold in 5 minutes after the gold starts running, which is why people told me it's horribly bad idea to go back so early. If you are rushing Sightstone it's no point going back at this point, because you can only afford Ruby Crystal and 1 Sight Ward and then you'd need to wait a long time to get another 500ish gold to get a Sightstone.
If you rush Sightstone you have to stay in lane for about 9-10 minutes before going back unless you get kills/assists. (972 gold at 9 mins.) If you plan on staying this long on a lane, you need them potions people suggested me.


Differences between the core items



So here I did the math about the difference with these two builds and how it differs in total gold gain, amount of wards and other stats right from the start up to 10 minutes into the game after gold starts running.

My Items at 10 minutes:
philosopher's Stone sight wardsight ward (and Mana Potion)
Total amount of wards: 6x sight wards, 2x Vision Wards and 1-2 Mana Potions
Gone back 1-2 times, 1st time at ~5 mins, bought a Philosopher's Stone.


The ward/Sightstone rush after 10 minutes:
(+ the wards you started out with if you didn't use them all yet)
Total amount of wards: 3x Sight Wards, 2 Vision Wards, 2-4 Ghost Wards.


Conclusion:



Basically you can get Sightstone playing my way only 3 minutes later than the other (which has earned 324 gold in 3 mins I waited for Sightstone).
After these 13 minutes with my way having a Philosopher's Stone since 5 minutes, you'll keep getting slightly more gold afterwards, whereas with only gold masteries you'll be getting less gold from that point onwards excluding last hits, assists and kills.

With my start at 13 minutes you'll have 468-324= 144 difference in gold and 1 more item than with the Sightstone rush. In total with a Philosopher's Stone you lead with

5 min without philo 780 + 7 min with philo 1092 = 1872
- 1,8x60x13= 1404
= 468 gold

Total difference in earned gold so far is 468 gold.

Obviously this just the most basic way of calculating the difference between using Greater Quintessence of Gold runes and Philosopher's Stone and not using neither and it doesn't apply like this in the game, because supports kill wards, get assists, kills and even last hits occasionally so you'll most likely get all items listed above earlier, but in the case you get into a game where absolutely nothing happens before 15 minutes into the game (that happens sometimes), you'll have a headstart compared to the other support.


Other semi-irrelevant notes:



Sure, early game you lack vision, but I think people can manage to play safe for 5 mins. I don't like to aim for kills before farming properly and getting at least lvl4.

Another point I'd like to make that I tried out Faerie Charm+2x Sight Wards+ Vision Ward+2x Potions started which is really popular as well opposed to these, but I have to say that this way puts a support way behind unless you do aim for kills. In case you're forced to go back early you can't afford anything else than Rejuvenation Bead and Wards and not rushing Philo when starting out with either Faerie Charm or Rejuvenation Bead WILL put you behind in goins compared to the other support or compared to either of the starter ways listed above.
I'm aware I have this starter in my Janna guide, but when I have the time I'm sure to change it into something else.

If you managed to read this, feel free to comment. If you find some totally gamechanging mistakes in my calculations, let me know. Like I said I don't usually spend 4 hours calculating stuff and formatting it into a relatively readable form for people who question my choices, but this is all for those people who think my arguments don't have any point. If you still feel that way, then I at least tried. :)

No hard feelings.