Fairy Power Spray - mainly for stains on surfaces; spray, leave for less than a minute, and wipe. Works really well on our light worktops that get stained by curry spices! Also good for cooked in/stubborn bits on dishes and pots.
Dettol anti-bac wipes - wiping up food/drink spilled on the floor, wiping down the surfaces, wiping down the high chair... and so on.
Bicarb & vinegar - for so many things 
Particularly for cleaning the sink and plughole, but also good for carpets (bicarb only!), odour neutralising in the bin or fridge, descaling a shower head...
Thick bleach - pretty much any brand tbh, I just look at the offers, but I find a thick bleach gets the toilet perfectly sparkling. Squirt, leave, flush later and it's all done.
Microfibre cloths - for scrubbing, polishing, drying, cleaning... I have different coloured ones for each room (kitchen, bathroom, general) plus one for glass, which I use on the mirrors.
These are the main ones that get used all of the time. If you have a shower with a screen/doors then I find keeping a shower spray in there always is good because if you spray straight after your shower it prevents the build up of limescale and keeps it looking clean.
As for storage, I have a plastic basket from Wilkos in the hall cupboard with them in.