1. I'd have one of those powers that isn't one big power but a collection of peak/above human (not super human) traits, above human strength, speed, relexes, staimina, healing and senses (hearing, smell, sight, even taste). So I could throw a guy whose 100kg, but can't punch through concrete. Can hear someone sneaking up on me but can't hear a pin drop.
My eyes would be yellow and my powers would be amplified/negated by the moon cycle, so on a full moon I'm extra strong etc, no moon just an ordinary guy.
I would use guns (but loaded with not lethal rounds) and ride a motorbike. I would carry gadgets despite my powers like tracting devices, stun grenades, expolives etc.
Eventually, after a couple of decades, a alternative universe earth (and its moon) would appear and try and enslave earth our pristine (by comparison) earth. The additional moon would supercharge my powers, to superman-esque levels and their earth would be destroyed, but their moon remain and adjust to our orbit, leaving me supercharged.
2. Hero and I'd fund my crusade against crime by appearing in adds and guest appearance on tv shows, anything from sitcoms like "thats how I met your mother" and serious shows like "house". But I would NEVER put advertisements on my costume.
3. Wolf and variants of that (depending on possible alternative costume and gimmick) with a prefix Blade- Lone- Silver-
4. Grey bodysuit with a silver crescent moon on the chest, silver wrist bracers, grieves and pauldrons made of several segmented plates overlapping. Gambit style mask, with a set of silver tactical goggle, worn on the forehead unless driving/flying/analzying date feeds sent to them.