Here are things I have actually used as an airplane owner...
Cleaning supplies:
Microfiber towels- get lots.
Your chosen washing soap/stuffs. I actually use a dry wash/wax once a year just out of convenience. Others use typical car wash soap/wax products.
Windshield washer fluid(the bug remover kind)
Spray bottle
Helicopter Polish(spray can) Arrow Magnolia is the manufacturer I think.
What you do is fill up a spray bottle with the windshield washer fluid. Then after each flight(at least in the buggy seasons) is spray down the leading edges of the wing, horiz stabilizer, wheel pants(if applicable), spinner, front of the cowling... basically all front facing surfaces that get bugs then wipe them down with a microfiber cloth.
On the windshield use the helicopter polish.... spray on, rub in good, let dry, polish off with another dry microfiber.
Hangar supplies(if you have a hangar):
Trash can
Push broom(widest you can get)
lighting.... I had a work light. Your need for this may vary with your hangar
extension cords
For cross-country/overnight trips..
Good set of ratchet straps for tie-downs. Some airports supply rope, most do not. If you're a good with knots, rope is fine. I don't trust my own knots.
A good multitool... pliers/screwdrivers/a blade.
Flashlights
Tow-bar
Rags
Spare oil
Spray bottle/helicopter polish/microfiber cloths so I can clean bugs away from home
One or two old sectionals(unfold, tuck under sunvisors and have a great window shade while parked)
Means to recharge phone/tablet
Beef Jerky(this goes in my flight bag, never go on a cross-country without it)
Water bottle
I don't carry chocks, never have. Most FBOs have them and will chock your airplane without being asked. If you are tied down, then you don't need them. If you're just stopping for lunch or something and the FBO doesn't have them, use the parking brake.
For cold weather(meaning below and well below freezing weather):
Any cold weather kit your aircraft may have/need and the tools to install/remove it yourself.
A switchbox to turn on the pre-heater by remote
An insulated cowl cover if it may be parked outside... extension cords also not a bad idea
Cleats that slip over your shoes so you can get traction pulling it across an icy ramp
A small ice pick and hammer to remove tie-downs encased in ice
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MONEY