Different kind of rechargeable battery chemistry requires different kind of storage procedures so that the batteries do not get damaged when they are stored.
In case of NiCD rechargeable batteries it’s advisable to discharge them completely if you want to store them, the quickest way to damage a NiCD batteries is by leaving them on a charger for extended periods of time (being topped) or storing them in a charged state.
In the case of NiMH batteries the best way to store them its to partially charge them around 30 – 35% …

You are right that your normal Dry cells and Alkaline batteries are advertised as 1.5v compared to NiMH / NiCD rechargeable that give an output of 1.2v but you should be able to use most of your devices that are advertised to work with 1.5v batteries should work perfectly fine with rechargeable NiCD / NiMH batteries that give 1.2v because the important thing to note regarding the voltage of a battery is the voltage output  a battery provides to your device when it’s under load.

There are a lot of different types of battery charges for various type of batteries, but I am going to discuss only about “AA / AAA” rechargeable battery chargers for the NiCD and NiMH batteries, these battery chargers are mostly divided into three categories dumb chargers, smart chargers, Battery manager (charger + conditioners + analyzers).
Do note that you should not charge NiMH batteries in a NiCD chargers, but most of the NiMH chargers can charge NiCD rechargeable batteries, also do note that investing in a quality charger is very important as …

I recently opened a new pack of “AA” size NiMH eneloop battery pack, based on the manufacturing date the batteries should be around 10 months old, so I thought that its a good idea to test the LSD NiMH (low self discharge batteries) claim made by Sanyo Eneloop batteries, these batteries capacity is rated at 2000 mAh when fully charged. The manufacturer claims that these LSD NiMH batteries should hold 90% of their capacity after 6 months and 85% capacity after 1 year of storage.

What is reconditioning of a rechargeable battery?
Reconditioning of a rechargeable battery is a process by which you regain the lost performance of a battery, If your rechargeable battery is not holding the power it used to you can mostly get the lost performance back by reconditioning the battery (exercise the battery) to restore the optimal performance of a battery, generally NiCD batteries required conditioning with every charge, but it’s not the case with NiMH batteries.

If you have been using NiMH rechargeable batteries for some time you might be familiar with the issue of these batteries getting discharged by themselves if  left for a couple of weeks / months, though all batteries self discharge with time, the rapid self discharge is a major problem with NiMH batteries they lose almost close to 1% charge every day and many batteries get discharged within 1-4 months.