Ran some console commands in the name of Science!
First, I leveled light armor to see the effect that skill has on armor rating.
Imperial Armor chest
- 25 armor at 15 skill.
- 33 armor at 100 skill.
Well, that's underwhelming. The rest of the numbers in this post are with 100 light armor skill.
Then I maxed smithing and started crafting.
- 74 - 4 piece leather - no perks
- 119 - upgraded with 100 smithing
- 238 - agile defender 5/5 (cleanly doubled the value)
- 357 - custom fit, matching set (and another 50% on top)
So much for unperk-able leather. How about elven?
- 297 - 5 piece elven armor, agile defender 5/5, custom fit, matching set
- 528 - upgraded with 100 smithing, elven smithing perk
- 610 - upgraded with 130 smithing by using Ring of Smithing (+15) and Necklace of Smithing (+15), elven smithing perk
- 537 - same, but shield-less
Elven armor is the lightest armor I'm aware of. 4 piece is 7 units of weight. 5 piece is 11 units of weight. With this low weight, you can easily skip armor weight reducing perks.
Then I headed off to the enchanting station for one last test. I enchanted with fortify armorer and saw no change to armor rating after the enchant. I recommend skipping the arcane blacksmith perk if you are planning to wear only your own crafted armor. Just upgrade before enchanting. (Ignore what the enchanting table tells you about armor rating, it's wrong.)
That's 2 smithing perks, and 7 light armor perks. With 100 skill in light armor and smithing, you'll be level 26 and easily able to afford these perks.
Can you skip the 2 smithing perks? Possibly. You'll need to compensate by raising smithing skill (much) higher, but if you're already choosing enchanting perks and/or alchemy perks for other reasons...
You can reach 610 armor rating with 9 perks and minor un-perked assistence from alchemy or enchanting. 567 is the armor cap.