Neil, cool dry place for the detectors. Never too hot or too cold, so that rules out attics or garages, and be careful with basements if they get damp.
For the batteries, rechargeables are like cars. The worst thing you can do with them is let them sit for months or years without being used. Far better to cycle them in and out of use with your other packs. But if you do store them, I haven't really read up on long term storage of nimhs or nicads, where as lipos are supposed to be put to a specific voltage called a "sleep charge" that has been found to be best to retain their capacity carrying abilities in the future when charging/using again.
With my lipos if I don't intend to use a pack for months I use the sleep charge mode on my charger which will then automatically either drain or charge the pack to get to the wanted voltage to put it to sleep, and then I'll store the batteries in a metal box in my refrigerator. The inside of the box is painted with non-metallic paint to prevent shorts, and I lined the box with cut up dry wall so that each pack has it's own "room" to sleep in. That way, should a pack go nuclear chances are it won't take others with it, because drywall is non-flammable. The lid of the box also has vent holes to vent any fastly escaping gas of a pack that explodes or quickly vents, without blowing the lid off the box. If anybody stores packs in a refrigerator be careful that the box doesn't start holding condensate (moisture).
I store my nimhs/nicads in the box too, but to be honest I haven't really read up on long term storage of those in years. Just not as concerned about nimhs/nicads since I have a ton of those types of cells and packs floating around for future use. Much more concerned about properly exercising them with 3 to 5 drains/charges in a row once or twice a year to insure they've got plenty of exercises to increase capacity to optimum levels.
But, I think from what I've vaguely remember reading long ago nimhs or nicads should be stored with some kind of charge, like perhaps half full or such, but in reality they self drain while in storage so I would guess then they'd need to be re-charged once or twice a year maybe. When a nimh or nicad goes completely dead and sits for long periods of time, there is a chance the poles on a cell or two can reverse in polarity. This is why many feel when exercising them they should never be drained completely, but I've never had issue with that and feel it's important to do so (MO) to get full capacity potential out of them. Kind'a like draining all the old gas out of a tank before putting new gas in.
Also, I think they say that once given (probably) half a charge or so, they should be stored in a refrigerator if I remember right (been years since I read up on storage of nimhs/nicads). I do store my nimhs/nicads in my refrigerator, but more so for reasons of fire safety in that metal box with my lipos than any real concern about long term health. I've got so many packs around, and so many Energizer 2500ma AA cells that I was given a bunch of, that I'll never be able to use all these things anyway before they go south on me.
Besides, those Energizers were from back about 7 or 8 years ago when they had a bad run of them that quickly drain day in days after charging, even much faster than what is typical for nimhs sitting on the shelf. These days they have low self discharge nimhs so I kind'a want to "use these things up' anyway to give me an excuse to pick up some new LSD (low self discharge) cells.
Used to keep my GT in the garage year round, until I realized a good hard freeze might say bust the LCD screen on the meter (doubtful), or the dampness in there at times isn't very good for electronics, along with very hot days when it could be 90+ degrees in there. Now that the Sovereign has been discontinued I've got to start treating this thing like a classic car that doesn't see rain. Very hot or cold days I'm not concerned about hunting in, but moisture for sure is an enemy of electronics.
PS- Batteries Again....I've had people give me cordless drill packs that have sat dead as a door nail for 20 years in their garage, to the point where the "charger" that came with their drills wouldn't recognize them to charge. My chargers will force them to wake up, and after about 5 to 7 charge/drain cycles in a row I often get full or even higher capacity than the label says out of them. Any time a cell will hold more capacity than the label says that's a good indicator the cells are in real good shape.
Besides cycling them, I'll often blast charge them at super high amps (say 5 amps for a 1000ma pack) for at least a few minutes to break down any resistance crystals that can resist charging and also lesson capacity. Or, sometimes if they won't take a charge people will shock them with say about double the voltage intended for re-charge, like say 24 volts for a 12V pack. Not something you want to do for more than a few seconds to bust the crystals down, and even then it's a risky thing and safety goggles/gloves/etc should be worn.
Even with the aggressive charge I'll give a pack, at super high amp rates I'll only risk that a few minutes and then go back to say a 1C rate (1 amp for 1000ma pack). Especially if the stock charge for the pack only does very slow charge rates of say 100 to 300ma for that pack. Usually a pack can handle 1C without stress, but I always check it with my hand for heat to see if it's complaining. Then, after 1 to 3 charges like this and drain downs, I'll flip back to a much slower 250 to 500ma charge rate or so.