My gosh, this is quite a complicated question. I mean the whole reason I love New Vegas so much is the sheer multitude of weaponry and armors and their combinations and permutations. I do personally not mind that armors have strange stats applied to them. It gives more meaning to different outfits other than them just being clothing you wear. Then we only have armor for armor's sake and I like getting at least some kind of bonus that's flavorful, not necessarily sensical
Back to topic: My favorite piece of any kind of equipment is the Stealth Suit Mk II probably, or as I like to call it, the Waifu Armor. It's voice is a pretty great way of differentiating itself from other equipment, even if it doesn't necessarily fill it's own role that well or protect as much as other armor. It just feels good to have my armor talking back to me and I barely register why. Other than that I really do enjoy the remnant armor and Joshua's, but a lot of other's appeal to me as well. The Armor of the 87th tribe I think is really nice to wear alongside the Blade of the West (A weapon I consider to be one of the 3 top tier weapons for melee, in my opinion.) My favorite guns would be either A Light Shining in the Darkness and the Survivalist rifle, both for reliability and simplicity. I was once also partial to the Ranger Sequoia before the DLCs were out. The Vault 34 security armor also gets a special place in my heart too. When it comes to energy weapons, though they are somewhat few and far between, the Plasma Defender will also be a mainstay for me. It simply looks amazing and is rather useful to boot. Most faction armor is rather nice in my eyes, but none of them truly stand out more than Papa Khan's Armored Leather and Helmet. When it comes to power armor, even though I stated earlier I liked the Remnant, the Scorched Sierra armor comes out on top in that department with me choosing it over any other power armor when I've had the chance. Then when it comes to just clothing in general I do like the Sheriff's duster, because who doesn't want to be the Sheriff in the Wild West Mojave desert (instead of say Wild Wild West Washington DC).