Exterior maintenance needs surprisingly little equipment, and the items that earn their keep are mostly unglamorous. The expensive things are used once a decade, which makes them hire items rather than purchases, and the cheap things are used constantly.
What follows is the honest division, based on what actually comes out of the shed more than once a year.
The things used every time
A pair of binoculars, which does more for roof maintenance than any ladder. A sturdy bucket and a stiff hand brush. A narrow trowel or scoop for gullies and gutters. A good hose with a lance, for flushing drainage and testing where water goes.
A screwdriver for lifting gratings and testing timber for rot, a torch worth the name for lofts and chambers, and gauntlet gloves, because gutters and gullies contain glass, nails and worse.
Measuring and recording
A spirit level long enough to be useful on a path, a tape, and a plumb line for checking whether a wall or a stack is upright. Chalk for marking hollow render, and a pencil for dating a crack.
A notebook and a camera. Those two find more faults over a decade than any tool on this page, because they turn a vague impression into a comparison.
Access, which is where the money goes
A decent ladder of the right length for your house, with a stand off bracket so it never rests on the gutter, is a genuine purchase. Buy the length you need rather than the length that fits in the car, since a ladder that is too short is the direct cause of the sideways reach.
A tower is a hire item. For any job occupying one position for more than a few minutes it is both safer and faster than a ladder, and hiring one for a weekend costs a fraction of owning it.
Hire rather than buy
Towers and scaffold, a pressure washer if you have decided you genuinely need one, a plate compactor for relaying paving, drain rods, a moisture meter, and a disc cutter. All are used rarely, all take up substantial space, and most are better quality in a hire shop than at a domestic price point.
Drain rods are the borderline case: cheap enough to own, and the one tool you want at ten o'clock at night rather than when the hire shop opens.
What stays in the box unused
Multi tools bought for a single job, cheap sealant guns that will not hold a steady bead, bargain brushes that shed bristles into fresh paint, and any tool bought because a job seemed imminent and then did not happen.
Spend the money on the things in constant use instead. A good brush and a good sealant gun make a visible difference to the finish; a cheap one makes the work slower and the result worse.
Consumables worth keeping
Exterior filler rather than interior, exterior sealant, kiln dried sand for block paving joints, timber preservative, and a tarpaulin large enough to cover something properly in an emergency. The tarpaulin is the item most likely to prove its value unexpectedly.