Ok, so this is just an overveiw... cause there are 100 ways to skin a cat and 1,000,000 ways to go logging...
Remaining safe, be alert watch everything, trees fight back and they are sneaky ****s. Broke limbs will fall without warning, logs roll for no reason at all, trees fall the wrong way, or split (barber chair or just chair) when being cut. Machinery can break in new and interesting ways, cables can snap or get cut turning several tons of wood loose, about the only thing you can do to stay safe is be alert and be ready to move, always have a plan b and and escape route.
Personal gear:
Hard hat (called simply "hat" or if its an aluminium "tin hat" on the west coast anyway)
Caulked boots (tough leather or rubber boots with hardened steel spikes in the soles for traction on logs and brush) often called just caulks, or calks, or caulked shoes usually in a very tall boot mine range from 14"-16" tall.
Tough denim pants either double front or single front, tough this bit is more a personal choice, but dickies and the like don't hold up to logging, often folks will cut the hem off so if yer pants get snagged they will tear instead of tripping you, it also helps them dry a little faster, some folks will stag them off quite high like halfway up the shin.
Hickory shirts are the norm out her, tough cotton shirt with small very fine blue and white stripes, from a few feet away they look light blue, its a regional thing as well. Though they are a very tough shirt and put up to a boat load of abuse, available in button front or a half zipper version, these are often stagged as well, mostly cause long sleeves are ****ing hot... that and you never know when you need TP...
Chain Saw chaps, kevlar lined cover the front of yer legs as well as the important sensitive bits, designed to clog up and stop the chainsaw chain from spinning and whacking yer leg off... (saw chain is very sharp and spins very fast, not much can stop it and yer leg will take a few moments to realize its not attached anymore)
The above covers just about all logging activities, except chaps... just need those when running a saw.
For falling timber, yer also going to need:
Plastic wedges 3-5 of em (arguments will start over how many and what type)
A square polled fallers axe for driving said wedges and various other duties like hacking bark off of thick skinned trees and freeing up a pinched saw
Saw gas 1-2 gallons
Bar oil 1 gallon
water 1-2 gallons (fer the poor ******* that has to carry all this stuff)
First Aid kit fallers are generally on their own, 2-4 in an 80 acre site and 200 feet or so apart so we don't kill each other with falling trees, Generally speaking the cutters start weeks in advance of the machinery, if something where to happen it would take a very long time for one of the other fallers to A notice and B make their way over to you.
A radio so you can communicate with the rest of the crew
and a big ole chainsaw, (also a thing that has lots of fight worthy oppinions) on the west coast its a 70-90cc saw with 28-36" guide bar, or bigger though bigger is sort of unnecessary anymore. The saw is used for the falling of the timber.
All together the fallers is carrying about 40-50#s of extra junk around with them in the woods, granted the gas oil and water can be left somewhere nearby until needed, the saw alone weights right around 20 pounds, each wedge about .5 pounds, axe 4-6# etc...