rechargeable is nice cause they do produce a higher lumens but if you go that route in my experience I would try to find something that can run on both AA batteries and a rechargeable cause nothing is worse then being in the middle of something or a trip that is taking longer then expected and to find out the battery is starting to die and no means of quickly throwing in new batteries in and continuing. just been burnt a few times where the light has died and need time to recharge. something to look into. plus make sure the on off button has some resistance to it so in the case if its in your pocket or bag and rolls over onto the button it doesn't turn on without you knowing about it.
I have a very decent flashlights, just this week I picked up a Fenix E16 (along with a little lantern which takes the same CR123/rechargeable 16340 batteries)
This thing is fantastic, 2" long and a maximum output of 700 lumens (700!) off the 16340s for up to 1hr 5 mins, has some other appealing features too for an EDC illuminator, I'm well impressed.
I have others taking AAA, AA and one that takes a 18650, mostly Fenix and this E16 has amazed me