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...
TLDR:
You can reach 610 armor rating with 9 perks and minor un-perked assistence from alchemy or enchanting. 567 is the armor cap.
I really don't see how you can beat Breezehome in Whiterun for the combination of features and time.
While there is a loading screen, it's extremely fast even on my slow laptop (which is below the minimum specs for Skyrim in several ways) and it's just a few steps from the fast travel location.
There are two sacks on the shelf right by the door you can reach without moving once inside.
There are plenty of other containers for sorted, more long term storage. You can get the "Well Rested" buff instead of just "Rested" since you actually own the bed.
It's definitely the most convenient of the purchasable houses.
Best Answer
Perhaps not the most efficient method, but this can be done AFK.
In Whiterun, just next to the accessory shop, you can crouch in a corner, behind the Whiterun guard. Hold the movement stick back*, so that you are "sneaking" backwards into the corner of the building. Leave the Console run overnight, and you will have 100 sneak by the next morning.
This is one of many places that this can be done, but basically, you just want to set yourself up in a location where you are in sight of someone, but can't be seen (the "eye" indicator is closed), and walk backwards (this obviously won't work if there isn't someone to sneak past).
Again, while not the most efficient in terms of in-game-time, it is in terms of your time.
User Kallum Tanton points out that the PC version has an "auto run" key (default C). This can be used by facing toward the wall instead.