Ihave two characters, dark elf battlemage is 16 and my nord thief is a 10. To this point I haven't found much of a difference. Maybe a person or two was abut nicer. They mentioned the fact I was a nord a couple of times. Not much of a difference so far, but it's so early to really tell. I believe the warrior stone only helps sword and board
If you want to tell the difference between each class type, this is what I recommend you should do, skip all other quests, and then do either of the following:
If you start a Warrior, go and seek out The Companions, and complete their quest line.
If you do an Archer / Rogue, seek out the Thieves Guild, and complete their quest line.
If you do a Mage, seek out The College of Winterhold.
If you follow the above, you'll get a true tutorial of each class in the best way possible.
In regards with the stone...
The Warrior Stone - Combat skills increase 20% faster. Any other starter stone (In the group of 3) is obsolete for the Warrior.
You'll find other guardian stones around the world which can benefit your class..
The Lover Stone - All skills improve 15% faster, is useful for being an all-rounder class.
The Lady Stone - Regenerate Health and Stamina 25% Faster. Great for melee combat.