From personal experience (the best!), I would say:
1. Footwear with good 'gripper' soles to prevent sliding on smooth - perhaps wet or muddy - surfaces.
2. Gloves might be handy if needing to do any climbing.
3. Two torches - perhaps one a wind-up - in case one is lost. Spare batteries.
4.. If going underground or around a factory, some form of headgear in case of hitting one's head against anything hard - rocks, ironwork, etc.
5. A camera of some type, but with a flash facility. Spare battery and memory card, if required.
6. A mobile phone in case of emergency.
almost spot on.
I use good boots, regatta walking trousers (these are ace, flexible & tough) & dark or camo top.
carry small camera bag with camera & tripod strapped on (dont need a flash if using tripod).
In the bag also fits 4 x spare batt, 2 x handheld torches & head torch & pair of light black gloves (yes deff needed for climbing particularly if there is anti climb paint),
also I use buff, gives a bit of dust protection but mostly used for camera avoidance.
thats my main kit, Iv spent years refining this & I honestly think it works for most things, its compact & easy to carry which I find really important, only downside I cant fit much food & drink in if Im expecting to be in anywhere for a prolonged time.
Underground is different altogether, I have wetsuit, caving suit, caving bag, derry drum, cow tails helmet to name a few.
Also in car I more often have 45ft rope sling ladder & grappeling hook... cos u never know ;-)
Oh & I just got some FB keys , may come in usefull.