If you do get a light that uses AA or AAA batteries, I would recommend looking into rechargeable batteries paired with a good high-quality charger. Search through the old discussions on this forum and you'll see a lot of references to Eneloop brand rechargeable batteries. They are HIGHLY recommended, and with good reason. My wife and I invested is a couple dozen of them about 8 years ago, and we have been using them ever since. I have yet to have any go bad, and they have great output. It takes a little while to get in the habit of popping them in the charger when they get low, but you get used to it. We've probably saved hundreds of dollars using them, not to mention the environmental benefit. Not sure about your household, but we use batteries for a number of non-caving applications as well, so even if you don't need them for your headlamp, you will likely use them for other things around the house.
Eneloops are made by Sanyo, and are available on Amazon.
We've had good performance from LaCross chargers like this one:
https://www.amazon.com/gp/product/B000RSOV50/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1If you get a light that uses 18650 batteries,then I would recommend Panasonic.
Trogman