All batteries have a shelf life... Shelf life is the time (after manufacture) over which and unused battery will decay and be non functional (Self Discharge).
The Shelf Life for Zinc Carbon (Indian conditions with elevated ambient / storage temperatures ) its 12 months and 3 years for alkaline.
Duracell Alkaline batteries sold in Packs on "SALE" are usually more than 1 year old ! (This brand also leaks terribly, but that is another story)
That is why All batteries will indicate their month and year of manufacture. Buy fresh batteries so that they last long in use, particularly light use (Clocks and remotes).
A Clock consumes Very very little power, so effectively the life of a battery in a clock is the shelf life of the battery.
A remote control also consumes power only when some button is pressed. Hence Ensure that you place a remote where no button will get pressed unattended (eg a remote on a table and a book is placed on top of the remote, pressing a button due to the weigh of a book, or the remote in a drawer cluttered with many other things.) Get a
Remote Control Stand from Amazon.
Rechargeable batteries, except the expensive Eneloop have very poor shelf life... Typically a few months.
Clearly it does not make sense to use a Rechargeable battery in a Clock or remote control.
The capacity (how much charge the battery will hold / deliver) is rated in Milli Amp Hours (mAh ).
Basic AA size rechargeable batteries will have a capacity of 600 mAh (ie they will deliver 600 milliamps for a total of 1 hour or 300 mA for a total of 2 hours).
Better rechargeable batteries will have a capacity of 1,100 mAh, and the current best will deliver 2,200 mAh.
The cost of the rechargeable will ofcourse increase with increased capacity. Usually, high capacity (better quality) rechargeable batteries will also have a higher shelf life.
A pack of 4 AA sized Eneloop Pro Rechargeable batteries will cost Rs 1,000+ or more than Rs 250 each. Would be a shame to use them in a clock where a (Rs 15 ) ordinary Non Rechargable Zinc Carbon battery will last for 1 year.
Of the 4 applications listed by you, I would recommend the following:
Clock - Ordinary Zinc Carbon Battery Rs 15 each
Remote - Ordinary Zinc Carbon @ Rs 15 each or
Amazon Basics Brand Alkaline AAA size (Duracell leak VERY Badly)
Keyboard - Ordinary Zinc Carbon @ Rs 15 each or
Amazon Basics Brand Alkaline AA Size (Duracell leak VERY Badly)
Mouse - Rechargeable AA. If the Mouse uses the thinner AAA size, then use amazon Basics Alkaline since AA size rechargeables have poor performance.... My personal experience. YMMV