Think about what you are most likely to face, the problems that would cause, and what alternative options you already have or could easily get.
Power cuts - power banks for iPads, phones etc already mentioned. You could think about folding solar panels (for camping) to recharge those as next level - but start with charging from sockets and having them charged up generally.
If the power went out, especially in winter, do you have heat, light, and ability to cook?
You might already have blankets to snuggle under, hot water bottles to fill, possibly an open fire or wood stove to use. Think about just using one room in cold weather to reduce the need for heating (if the power is out), and close the doors to other rooms to prevent the cold moving around easily.
You might already have a torch, solar lights in the garden, candles for smells or dinner parties etc. Candles need to be carefully used in proper holders, away from draughts, away from children and always supervised (so the room you're in only). A camping lantern, especially a rechargeable one (using your power bank) could be useful to light the hall and stairs. A headtorch around a large bottle of water and facing inwards makes a surprisingly good lantern. You might already have the motion-detector type lights in your hall for DCs who wander to the loo in the middle of the night - if you use battery operated types, they will still work. Garden solar lights could be recharged outdoors in daytime and used indoors at night - they might not be very bright but will help and can help make it cheerful which also hugely helps. Also, don't underestimate the value of clearing the main paths around the house (kitchen to bathroom, living room to bedrooms, etc) of clutter so that there is less to fall over if the light levels are low.
Cooking. Do you have a gas cooker that still works if the power is out? Do you already have any kind of BBQ? We have a gas one that's been used for all sorts of cooking at all times of the year including when we've had power cuts. Putting a normal pot on it with water is slow but works to get hot water for tea/hot water bottles etc. You might need to give pots a good scrub after to remove smoke from the outside, but you can use them to cook as normal, on top of the usual grilling of meats, cooking things in tin foil parcels etc. Do you have a few cup a soups or ramen noodles that just need hot water to make up, or a few tins that need very little heating up or could be eaten cold if needed (baked beans, spaghetti hoops, chilli in a can etc)?
If the water stopped, what would you do for toilets and drinking? Do you have a water butt from your drainpipe outside that you could use for toilets? Do you have a cat, that you could make a toilet in a bucket using some of their litter in a black sack? You might have a couple of large pots or bottles to fill with water if you know there will be a cut, or get a few bottles from the supermarket to have in a cupboard just in case. A basin or a bucket might be useful to let you wash with a sponge if you can heat up a kettle/pot of water, and to wash up the dishes.
The other thing to think about is if you might have to leave the house in a hurry (weather, gas leak, house fire (you or neighbour), floods etc). What do YOU and YOUR FAMILY need for a couple of days, and what would you not want to lose? You might want to make a bag with a set of clothes each for everyone, meds for a couple of days for anyone who needs them, some emergency cash, and at least a photocopy of your important documents (marriage cert, everyone's birth certs, list of phone numbers of important people (family, GP, insurance company etc), list of bank account details and insurance policy numbers, etc. Any important medical notes (not actual files - but a sheet saying any long term issues family members have, meds they are on, contacts of specialists etc). Perhaps a couple of family photos for ID, or photocopy of passports, driving licences etc, but also a couple of actual photos of extended family and special moments (in case the bag is all you have later on - unlikely but can happen).
Pets - do you have any and what would they need?
Money issues - saving up money to have emergency funds ahead of time, or building up some supplies in a cupboard to dig into.
But it starts with the thinking about what is realistic that MIGHT happen to you and your family, and how can you make it easier to get through that issue by doing a few things now. And how can you use what you already have, before ever thinking about going to get new things.