Gecko-backed Leather-Armor, reinforced.
It looks superb(even better since I switched to the PC and installed FOOK, which gives it an own texture), offers decent protection, can sustain a bit of damage before falling apart, and the +15 rad resistance are enough to get to 85% when using Rad-X. So no Radiation suit needed at any time, which is a good thing.

I also like Graham's Armor for being extremely light(doesn't take a lot of a beating, though) and offering a crit bonus, I use that for LR, and the Sierra Madre Armor, reinforced.
When on the Strip I usually wear a set of Formal Wear, and put Cass into Vera's Dress.

Elite riot gear/1st Recon beret/lucky shades

I'm also partial to the assassin suit and Joshua Graham's armor.

Followers' Labcoat
Hellfire Power Armor
Daniel's Outfit
Leather Armor

I've finished my best armour.
Its a cross between Hellfire, dragonskin and riot gear.

Elite Riot gear armor with 1st recon beret (as a sign of disrespect towards the NCR) and Authority glasses.
OR marked Tribal armor and mask because it's the closest I can get to Legatus Lanius' armor.

Vault 34 armor is my favorite for practical reasons. It has one of the highest DT of light armor, and it is extremely cheap to repair.

Although for appearances I like the Chinese Stealth Suit with a Desperado cowboy hat. It looks like some sort of ninja cowboy.

Desperado cowboy hat, biunty hunter suters for a lone cowboy style
Space Suit
Assasin suit
Vault 34/dead moneys security armor

It depends, but my favorite sets of apparel would have to be either:

Courier Duster (independent), Slave Scarf, rebreather

Desert Ranger Armor, Daniel's Hat, Lucky Shades

or

Assassin Suit, Sierra Madre Helmet Reinforced/Hazmat Darklight Cowl (depending on light level)

Desert Combat or the Elite Riot with the Marksman slung and ready to go.

I loved Power Armor and Plasma Rifle in FO:3, but for some reason, the Desert/Riot armor and a 'Guns' weapon seems to be a better fit for the Mojave.

Assassins suit and ranger helmet

Stealth suit MK 2 and Elite Riot helmet
or
US army combat armor and combat helmet

The Raider Painspike Armor by far. Wish we could add like a bulletproof vest or to make our light armor DT stronger.

The other armors don't look post-apocalyptic enough for some reason. My other favorite is the Stealth Suit MK II, I love how it speaks to you and gives you med-x. Just wished they looked better.