Garth, here is my stash.
For headlights I highly recommend the Princeton Tec Apex series (Apex, Pro, Extreme), the grey and orange lights on the left of my picture. They have spot and flood combinations, various brightness modes with 200 lumen max output, strobe & beacon modes like you want, different batteries CR123 (Pro, the grey one) or AA (Apex / Extreme, the orange one), have a very small flashing led to find it in the dark, a battery level indicator (very important). They are very comfortable and very reliable. I use headlights more than flashlights to leave both hands free.
For flashlights I am blown away by my 4Sevens lights. They have very clean beams, are very efficient, small and are programmable with different mode & brightness preferences including the flashing modes (strobe, beacon) that you like. The best feature for me is the moonlight mode with only 0.2 lumen output (10 day runtime in that mode). It is great to use when you want very little light. There is nothing worse than having only a blinding, glaring bright light in a small space or on a close object. But with these I can switch from 0.2 to 190 lumen in an instant.
They are also super tough. I sometimes demonstrate by turning the light on, throwing it down from a standing position onto the carpet so it bounces back up and I catch it again without so much as a blip in the light. They have reversible pocket clips, sheaths and many other features. The polished Titanium ones are Limited Editions and there are also black aluminum ones. I am definitely going to expand my 4Sevens collection significantly.
I also have some Inova, Surefire and Fenix. Some people swear by Surefire but others feel they have been left behind. Fenix are also very good lights and I really like their quality and features but not as much as the 4Sevens.
One really good accessory for the Fenix lights is the light cone. It fits onto the end of the flashlight, turning it into a lantern. I now use that instead of my bulky lanterns for car camping.
I don't have any in-hand pictures to show size but here they are with some folders to give an idea:
Pelican also makes some decent lights and I will probably pick up a few. My Pelican dive light is probably 15 years old but still works with its original bulb!! I know it is overdue for replacement but it has too many good memories associated.
The Maglites are no longer in rotation

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I have not yet moved to using rechargeable batteries for various reasons but I will do so soon. I still use primaries (Surefire brand for CR123) and various for AA and AAA. I am no expert but Eneloop seems to be very popular with the guys on CPF.