Reaper is the best, but do you have LeDoux's hockey mask? It's basically unlimited AP, and never breaks. I ended up with that and Chinese Stealth armor, and even Deathclaws trembled hearing my name.
I usually go with the Ranger armor; it's got a reasonable stealth rating and it's easy to repair with merc armor, plus the small guns bonus. My big brother plays a tank-type character and always goes for the power armor at the earliest possible opportunity, but I find it too heavy to carry around all the time and can't stand the speed and stealth debuffs that come along with it.
I have LeDoux' hockey mask, but I don't wear it because I don't like the way it looks. I play a female character, and she wears horn-rimmed glasses and an Enclave Officer's hat. I don't usually have AP regen problems any more (sniper + concentrated fire + Reaper's sprint + high luck = fuck*ng BAD ASS) and usually I can KO several super mutants without taking a single point of damage, provided they don't have an overlord with them. (Those bitches are insane.)
On my restart I'm level six. Three intense trainings, comprehension (must-have), and toughness. I really like sniper. Bloody mess is nice for the damage add-on, but I kind of get tired of all my opponents exploding when I kill them. Anyhow, I'm looking forward to playing through it again. It's been months since I fired it up. I may open up my old guy and look over his skills today.
As I mentioned above, sniper + concentrated fire is awesome, especially if your small guns skill is anywhere near decent (gunslinger perk is nice in this combo too). I never took Bloody Mess, because I don't like searching all over the map for body parts. I hate when two or three people explode on a critical hit and you've got all these mismatched legs and eyeballs lying around and you have to click on them all looking for the one body you haven't looted yet.
I'm still messing with my first play-through because I took my good sweet time doing all the side-quests. I don't think I'll start again -- I like the character I ended up with, and while I'd take different perks if I had to do it over again (I'd ditch Mysterious Stranger and Here and Now for Comprehension and Swift Learner, for starters), I'm pretty happy overall with my character. Besides which, I'm looking forward to starting fresh with New Vegas (I picked up my brother's copy today, it totally sucks that I have to wait another month to play).
I took Nuclear Anomaly when I hit level 30 but I haven't had a chance to see it in action yet. (I rarely take that much damage in a fight.) Have you ever used it?