Is this even possible in the beginning? From everything I have seen it looks like the game favors the Warrior/Melee class and it is difficult to get good gear for light armor based players early in the game.

If you need to play a tad differently in the intro, so be it. The intro is maybe .01% of the entire game.

Regardless of what stone you choose, you can still swing a sword. And destruction should be fair at the beginning.

In the tutorial dungeon you get a Mage robe and Potions, scrolls and a Shock spell tome.
I'm sure you can get other light armor in chests in the dungeon.

If the game favored Warrior classes there would only be a Warrior Guardian Stone. Elder Scrolls games is centered around what you want to do.

My bigger concern is the availability of only Destruction and Restoration Spells right out of the gate.

You're telling me a weak Shield Spell, Summon Bound Dagger, and Starlight would be too OP for a starting character?

Whatever Bethesda.

Has anyone claimed they're OP?

Destruction and Restoration are the most popular, so they'll be the first people get. And depending on what race you chose, you can get another spell. Like Bretons get a conjuration, supposedly.

Bretons start with a summon and Altmer start with a frenzy spell...

there were scrolls? Do you remember which scrolls?