Right now im grinding resto and light armor, so far during the 20 some level transition I don't think that resto has gotten any faster or more efficient and if it has it's hardly noticable
Without perks:
For alteration, destruction, illusion, restoration and conjuration, spell cost (not power unfortunately ;- goes down up to -40% at level 100. Spell tomes also become available depending on your level.
For archery, two handed and one-handed, weapon damage goes up to +50% at level 100.
Light and heavy armor profit minimally from leveling. Perking is required.
Most skills don't get really good without perking.
Each point in armor skill increases armor rating by 0.4%. At level 100 that means 40% increase in armor rating. That's without the perks. The main armor perks (Agile Defender or Juggernaut) double the effect at 5/5 perks. I wouldn't call it a minimal effect without perks but they do help.
Still, most skills require perks to be effective. Magic is another matter, it's not particulary effective even with perks.
As far as I know, the rate either armor skill levels, depends on how much hard you're getting hit.
Restoration won't go up anytime soon, just by casting healing on your character. However, Whiterun's Hall of the Dead has 3 skeletons to cast Turn Undead on. This will get the skill going. When/if you have Repel Lesser Undead or even better, Repel Undead, round them up and start casting on them. The skill will max out in almost no time.