You only really need a few good cleaners for the whole house, sure all the new concoctions they come up with in the supermarket are "fun" to try I need a life, but they're not needed.
This is what I couldn't be without:
Good washing up liquid (this can be used to clean almost anything).
Bleach (I know a contentious thing, but I find I can't do without this for germ kill).
All purpose furniture polish (fave is Pledge) - as all-purpose, can be used on all sorts of surfaces.
Glass cleaner (mirrors and glass of course, and can be used to add shine to kitchen appliances - so can all purpose polish though).
Cream cleaner (not often needed, but if have a stain that won't shift - stainless steel sink mainly - this will remove it).
Bathroom cleaner spray/liquid (for sinks/showers/tiles)
Laundry + Dishwasher detergent.
Of course, a good set of cloths/pot towels, rubber gloves, a good broom (and dustpan and brush) and a good mop+bucket. Rubbish bags for the bin.
But by far the most important cleaning gadget you will ever own - a really good quality and versatile vacuum cleaner.
That is pretty much it for me, as in what's needed
Nice to haves (and I do have them)
Kitchen cleaner spray (but a solution of hot water + WUL + bleach in the kitchen sink and same solution in mop bucket would do entire kitchen - and actually the bathroom).
Disinfectant liquid (does same as bleach though)
Toilet cleaner (bleach can do same though).
Air freshener (not really needed, as if something is giving off an odour, that means it needs cleaning - if it is a room, it needs airing).
Mould/mildew spray (again - bleach kills mould).
I'm sure I've got others that I can't think of.
You may need some form of limescale remover (eg Viakal) if you live in a hard water area, I'm lucky enough not to though.