What is the best obtainable gear in Heavy Armor, Light Armor and Clothing?

The progression in Skyrim is not perfectly aligned by material (for example some steel items are better than some dwarven), however there is a general progression. The character classes in Skyrim are not as limited to armor type as in other games. Generally you will see more cloth items with caster enchants, but they show up on other armor types and you can craft whatever you like. Another example of this is that if you pursue high enough skill levels heavy armor will get to the point where it no longer impairs stealth and there is a spell to make it silent as well. It seems that the primary disadvantage to heavy armor is in carry weight and speed (can anyone confirm this?).

For Heavy Armor the best material is Daedric and for Light Armor it is Dragonscale.

The full Heavy Armor progression is (with very rough levels):

• Iron (lv 1)
• Steel (lv 6)
• Dwarven (lv 12)
• Steel Plate (lv 18)
• Orcish (lv 25)
• Ebony (lv 32)
• Dragonplate (lv 40)
• Daedric (lv 48)

The full Light Armor progression is (with very rough levels):

• Hide (lv 1)
• Leather (lv 6)
• Elven (lv 12)
• Scaled (lv 27)
• Glass (lv 36)
• Dragonscale (lv 48)

Clothing doesn't progress, rather the enchantments get more powerful as your level increases.

As already said, for heavy armor the best material is Daedric, but pretty close and much easier to get is Dragonplate armor. The base armor looks something like this

With 100 Smithing you can improve it to legendary and get something like this

But that's not the end, you can increase your smithing skill above 100 with enchantments and potions, with 3x 24% smithing enchantments and one 20% smithing potion you can get something like this

So you can more than double the armor rating by getting your smithing skill above 100. And what I showed just now is not the end, you could level alchemy to 100, use some fortify alchemy enchantments and create a fortify enchantment potion. Use that one to enchant your smithing gear and you'll get an even bigger bonus. You can also then brew a much better smithing potion than the 20% store-bought one I just used.

The most powerful (rating) crafted armor is at the top of the Smithing perk tree: Dragonscale for Light, Daedric for heavy.

Smithing skill doesn't change the rating when you freshly create the armor. Skill only comes into play when upgrading it. Get skill as high as you can when upgrading. See Fabian's answer.

Enchanting skill and perks affect the magnitude of enchantment you can place on the armor. I haven't seen any enchantments that increase armor rating.

As discussed on other questions, there is a 567 armor rating hardcap. Some say it's possible to hit that cap in Legendary Hide armor. If this is true, the main advantage of having Legendary Dragon or Daedric armor would then be to hit that cap with lower armor skill and fewer armor perk picks.

For weapons you want Daedric (sorry Glass users).

Smithing skill interacts with weapons the same way it does with armor. Don't need skill to make the item. Boost skill as much as possible when upgrading.

Enchanting can add damage to weapons. I don't have much experience with this, or the skill boosting opportunities involved.

In the Dragonborn DLC, there is a Stalhrim armor variant called Deathbrand and when all armor pieces are found and fitted together it gives a 100+ armor rating plus a +60 to stamina, and some other huge benefits which I forgot, it is LIGHT ARMOR and it's around 100 armor rating higher than Daedric at basic. It's also fully upgradable.

To be honest, you're all assuming we're talking vanilla Skyrim. Add in Dragonborn and the best Heavy armor becomes Stalhrim. stats as high as Daedric, weighs about same as ebony or less. Not to mention anything Frost based you add to it is 25% better because it's basically armor made from ice. It does require a quest to make/obtain though.

Not sure about Light Armor with Dragonborn, but if Dawnguard is in the mix as well, Vampire Royal Armor is your best bet for Light, although I've only seen four sets and theoretically you can only collect two of them. One from Lord Harkon, and one set found while exploring the castle for Serana's mother Valerica. Valerica and Serana's sets are not obtainable, due to them being marked as essential and therefore, unkillable.

My Dragonscale light armor is 218 after additional enchanting and smithing potions. I haven't been able to make any of the other armors that strong.

I tried optimizing both my alchemy skill and enchanting skill to 5/5 and make fort. smithing potions and fort. enchanting potions. Then I enchanted a set of helmet/crown, necklace, rings, and bracelet/gloves with enchanting skill and smithing skill (using fort. enchanting potion when enchanting). Once done, I went on to making a full set of dragonscale armor.

After using the fort. smithing potion when improving armor and weapons, the armor alone (with light armor bonus) got 508. In total I have about 1200 in armor points on the character with powerful enchantments.

I can and have achieved a billion+ armor rating, due to the spamming of Restoration Potions. My Iron dagger gets 7,573 damage, my enchantments are along the lines of 60,000 health, stamina and magicka using a petty soul gem, and I can unlock any door without moving the pick a centimeter.

It does, however, totally kill the gaming experience as there is no challenge.