Ohhh, Unarmed! I freakin' love unarmed! I had an unarmed guy at one point, he started as a Bar Brawler type, but moved up to Praetorian.
I would highly recommend jacking up Endurance. The extra unarmed damage is nice, but so is being able to take punishment seeing as you need to run into danger. Heavy Handed works nice. The other trait is up to you.
I would also highly recommend an agility of at least 7 so you can get the Slayer perk.
Take any unarmed perk you can! That much is fairly obvious. However, for some un-unarmed perks may I suggest Rad Child? The more you become irradiated, the more GODLY you get. I ran into a group of Rangers with Brush Guns and AMRs and I just ate their bullets for breakfast. Since I had a high endurance I could take extreme punishment, but because I was diagnosed with Deadly Rad Poisoning, I was near invincible. Not to mention you'll be swimming in caps since you can sell stimpaks and you don't need to buy them!
Taking Toughness is also a decent choice. Combined with Rad Child makes you even more of a tank! Also reduces the need for Power Armor for each rank.
Adamantium Skeleton ensures you are fit for combat- nothing svcks more than having your legs crippled while trying to chase down a guy with a minigun. Not fun.
For equipment, I would try to stay with Light or Medium apparel. Yes, the extra DT is nice, but it comes at the price of slower speed. Slower speed means you are eating more bullets. The only thing that should be eating bullets is you when you have Rad Child, not power armor. If you do choose light armor, try out Travel Light. It will help end battles that much quicker!
Also, try for Love and Hate at lower levels. At medium-higher levels, aim for a Ballistic Fist or Displacer Glove, or the Pushy/Paladin Toaster if you can. You could try earning Caesar's favor by getting access to his personal clubhouse and get loaded on Praetorian gear and the Lucky Shades.
This was the basics that I had used for my unarmed guy and it worked wonders for me anyways. No Ranger could stand a chance against me! I could also hold my own against Deathclaws and Cazadores. Best of luck!