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

Basically, one can get armor/weapons up to:

• Full Daedric Armor: 2125 Armor
• Daedric Bow: 562 Damage
• Daedric Dagger: 171 Damage
• Daedric Two Handed Sword: 605 Damage
• Daedric One Handed Sword: 518 Damage

Perks you need (33 perks):

• Heavy Armor (Juggernaut 5, Well Fitted, Tower Of Strength, Matching Set)
• 5 Weapon Perks (base, damage raising) of your choice
• Smithing (Steel, Dwarven, Orcish, Ebony, Daedric)
• Enchanting (5 X Enchanter, Insighful, Corpus, Extra Effect)
• Alchemy (5 X Alchemy, Physician, Benefactor)

Instructions:

1. Get max perks and 100 in each skill.
2. Enchant fortify alchemy helm, ring, gloves + necklace. The buff should be +25 on each for + 100 total.
3. Put on the gear and make 4 fortify enchant potions (+ 27ish?)
4. Use those potions to make better fortify alchemy gear. Note: you have to be quick because you only have 30 seconds per potion.
5. Use that gear to make better fortify enchanting potions.
6. Keep repeating 4 - 5 until you can make fortify alchemy + 29 on each piece (116 total)
7. Use 4 +32 enchanting pots to create fortify smithing rings, neck, gloves and chest.
8. Make some fortify smithing potions (+130% with your alchemy gear)
9. Craft daedric armor, shield and weapon.
10. Put on your smithing gear, drink the potion (130 + 116 = +246% to smithing), then improve your weapons.
11. Make about 10 enchanting potions (+32)
12. Enchant a ring gloves and neck with fortify heavy armor and fortify one handed. (I believe the number was 29 for armor 47% for weapon? Not in front of computer).
13. Enchant health / heavy armor to chest.
14. Enchant one handed / stamina to boots.
15. Enchant helm with whatever you want.

Source

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.