Many mineral collectors dislike the blue cast of an LED lamp and prefer to carry rechargeable battery lamps with incandescent bulbs. Many of these have the sturdy lamps with lead acid batteries that are used by modern day miners and geologists. Consider though that the battery is big and heavy and sized to provide light for an 8 hour shift (and a bit more).
You really should carry a backup light of some kind. These days, without question this would be another LED headlamp. And you should have a spare (fresh!) set of batteries for your primary light source. Cavers say you should have 3 entirely independent light sources, and I won't argue with them.
Regular incandescent battery lamps are OK for short forays. Flashlights are a general nuisance, but a small mag light can be a nice accessory. What I like even better is to have a handheld light that I hang on a lanyard around my neck. I recently bought a unit with a 1 watt LED and 4 AA batteries and a fitting for a lanyard and it is wonderful. I can hold it in my hand where appropriate and then drop it and let it hang when I am on a ladder. Something that is really handy is a well focused and very bright beam for occasional use. I once had an expensive "tactical" flashlight with an extremely bright Xenon bulb and which ran off a pair of large lithium batteries. It had a momentary switch and was just wonderful for looking down the occasional deep hole. What I didn't like was the cost and the need to use exotic batteries. It needed a place to attach a lanyard as well.
Petzl and Princeton Tec and probably my two favorite light makers. Petzl in particular caters to serious cavers and has many models that are reliable and well made.
There are many styles of hats. Perhaps the worst is the everyday construction hard hat (but it is serviceable and what I have used for a long time). An actual miners hard hat has a brim all the way around, and a clip for a light -- these are great if you add a chin strap. The brim keeps dirt and stuff from going down your neck. What I really like is a globular shaped hard hat with a chin strap designed for caving or mountaineering use. Fit a lamp onto one of these and you are set. The chin strap is a big asset if you envision doing acrobatic rope work in mine shafts. It is pretty much optional if you just plan to stroll down drifts and climb up and down a few raises now and then. If you ever did take a nasty fall, a good hard hat with a chin strap could save your life.
Once you have a hard hat, you are facing the decision of how to attach your lamp. This is less of an issue if you just decide you aren't gonna use carbide lamps, since most LED headlamps attach with an elastic strap. You would then want to back up the friction of the elastic with perhaps Duct tape (really ugly), or a bit of cord as I have done. Get all this worked out before you go underground.
If you are for some unexplainable reason thinking of using carbide, you will need a hat with a bracket. When I had a mountaineers helmet and decided to attach a lamp bracket, I just went to a store in town called MSA (Mine Safety Appliance) and bought the bracket. Then I voided the helmet warrantee and engineering and drilled two mounting holes for the screws. I suppose if I got hit in the head by a falling anvil, the helmet would have split in half along the holes I drilled, but oh well.
I recommend the first approach (no rope) unless you have actual training and experience in technical rope work. A rope can give a false sense of security and tempt you to get yourself into trouble that you would simply steer clear of without it. Technical rope work is incredibly time consuming. If you are interested in it, practice above ground first and read read read and practice practice practice until you are quite comfortable with everything involved before going underground.
I have stuck this section at the end, because it is really an ode to a bygone era. Carbide lamps are becoming historical artifacts, but they are fun to fool around with if you can get your hands on one and on the carbide needed to fuel it. You need to enjoy tinkering to use one. They put you in touch with what it was like to be a miner in the grand old days.
Carbide does have certain advantages. It gives a widely dispersed light instead of a focused beam, and it gives some information about air quality and the oxygen content of the air you are breathing. With carbide, you get 2 hours of high quality light per load, and it is easy to carry enough carbide for a full day underground. In the days before LED headlamps this was quite an advantage over electric lamps which required you to carry an unreasonable supply of batteries to feel adequately supplied with light.
Remember too that you also need to load the lamp with water and don't guzzle everthing in your canteen! Maybe a second water bottle just for lamp water would be a good idea, but I have never done this.
With carbide you should carry an extra ceramic lamp tip and some kind of reamer to clear clogged tips. What works well as a reamer is to cut a bunch of 2 inch lengths of stainless steel wire rope (if you have a bunch of this in 1/8 diameter laying around as I once did, and the tool to cut it). Then crimp a wire terminal on one end and you can hang this on a lanyard. Speaking of lanyards, you should rig up some kind of lanyard from your lamp to your hard hat in case the lamp gets knocked loose. I had this happen when ascending out of a very deep vertical shaft. This left me in the dark hanging on a vertical ladder over a very deep hole. A fished a piece of climbing sling out of my pack and tield myself to the ladder and switched to the electric light in my pack. The lamp landed right in front of my partner, who retrieved it -- but the ceramic tip had popped out of it and it was useless till I got it back to town and bought a replacement (and a spare).
The subject of carbide lamps gives a chance for a story. A buddy and I were down in a mine in the Inyo Mountains where we ended up spending all day underground. I was in a stope digging around for specimens, and my buddy was exploring the rest of the level (yes we really should stay together, but we didn't). Of course my carbide ran out and I didn't have a spare lamp (we had grown confident of our ability to fix anything that could go wrong with a carbide lamp in the field). I had gotten used to just changing the load in the dark. First I would set out the things I would need so I could find them in the dark and they weren't going to roll off somewhere. A nalgene bottle full of carbide, a canteen with water, a stick to scrape spent carbide out of the lamp, the reamer just in case. Then I would blow the lamp out and find myself in total darkness, then change the load by feel (this is actually really cool and fun). I would refill the water by filling my mouth and transferring the water into the lamp so nothing would be spilled. Then the magic moment of cupping my hand over the lamp and stroking the flint and with a pop noise the area was again filled with light!
On the same topic, when we would be roping down a shaft, we would travel one at a time and the first guy down would get off to the side in a level and yell up that he was clear and the next guy could start down. I would always get in a safe spot and turn out my light to conserve batteries or carbide. I can remember many times sitting in the dark and waiting, hearing little sounds, things rattling past, a ting-ting of my buddy bumping against a pipe, then there would be a hint of light, then more and some legs would show up and he would be wondering where in the world I was since I was absolutely quiet the whole time, then I would hear, "Oh, there you are -- where does that lead to anyway" and off we would go again.
And something should be said here about ropes and carbide lamps. In short, they are a very very bad combination. I will NOT use a carbide lamp while ascending or descending a rope. It is just automatic to stand there holding the rope with the flame from the lamp on your head burning the rope. Sure, attention to this can avoid the problem, but it is a nuisance and sometimes you just need to be paying attention to something else (like not getting killed). enough said.
Tom's Old Mine Info / firstname.lastname@example.org