bleach for toilets, couple pairs marigold rubber gloves, disposable cleaning cloths and sponges, toilet brush for each toilet u have, bath/shower cleaner.
Cloths/brush for washing dishes, hand soap, oven cleaner, surface antibac cleaning spray.
A personal recommendation would be sonic pest control devices, 2 should suffice in either end of house to keep unwanted guests (rats/mice) away from your home and general property area.
in terms of cooking utensils, you dont need a huge knife block set to do what you need in the kitchen, a good investment if you can afford is a good quality chef knife (you can do 90% of your cooking requirements with this), a small paring knife for veg/fruit, bread knife and a sharpening steel. A lot of folks invest in 10-32pc knife block sets and half, if not more goes unused, those 4 essentials, cared for correctly will last you a lifetime and do most what you need at home.
Stainless steel pots and pan will last you long time, if buying non stick pan, invest in one that is pfoa free (harmful chemical) such as tefal, but stainless better for heat distribution and long lasting if you take care of it, metal handle pan you can also use in oven.
If you going to look for something like a deep fryer, i would suggest looking into something like a multi cooker that can pressure cook, deep fry, rice cook and so on. Good investment in 1 tool that does a lot and you will use more regularly, rather than spending on a lot of equipment that may get used sparsely. (good space saver)
5l bottle of distilled vinegar, weird one to throw in but mixed with salt and water it kills weeds, mixed with water cleans tough stains, good on chips
Thats all i can think of now, but i would suggest putting all the items suggested by everyone into an excel document (put the brand you going for into 1 column, size/quantity in next and then cost in last column) do a sum formula to identify your costs, then decide which is most important to you immediately and you can knock stuff off the list as you go.