I know some of these have been mentioned but it helps my train of thought to just run them out.
I wouldn't want to be without:
~ lawnmower
~ garden hose
~ shovel
My prefrence is a spade as I've found the need to dig is more prevelent than just moving things. (plumbing lines, tree roots, turning over the garden, burrying dog poop, ect.)
~ some type of saw
(I am guessing you have a basic toolkit with screwdrivers, hammer, wrench, duct tape, yada yada. If not this is a must)
To seriously consider:
~ decent size/quality snake
~ weed wacker
~ snow shovel
~ upgrade the above from some type of saw to a chain saw
~ rake
Services:
~ Garbage
Will you need to pay?
Are there competitors?
Are there seperate fees for yard waste?
Does the area have free drop off days?
Do you have to supply your own cans or do you have to rent them?
~ Water
Figure out the average water bill for the area?
Are you on sewers?
If not, find out what you have. ( septic tank, laterall lines and so forth) Once you know what you have look into fees associated with it.
Also, if you aren't on sewers you may want to find out if your area will be put on them anytime soon. Some places requier everyone in the section they're adding sewers to, to hook in, in a certain time frame and that can run some serious cash.
~ Heat
Are you oil burner, gas (from the gas and electric co.), propane, or electric?
Check into how old the equipment is and search into fees and maintanence.
(We had an oil burner growing up on L.I. and when the prices spiked the SPIKED and when the thing backed up one time we cleaned forever as the whole inside of the house got coated in black soot.)
AC
~ Are there window units or central air?
If there are window units you may want to ask if there is already duct work in the house that a cental air unit can be hooked to. If you go to add cental air and there isn't any you've just added a LOT of additional cost.
I'll keep thinking but that's a start.