Three wattage calculators gave me three different answers - how much power supply do I actually need, and does the brand matter?

The spread is real and it comes from what each calculator assumes about spikes.

Average draw is not what a power supply has to survive. Modern graphics cards in particular pull very short bursts far above their rated figure: brief spikes of double the sustained number are normal. Those last microseconds, so they barely register in a power meter and they absolutely can trip a supply's protection and shut the machine off. A calculator that only sums rated figures gives you the low number; one that allows headroom for transients gives you the high one.

So the sizing method:

Add the sustained figures for your components: the card and the processor are essentially all of it.

Add generous headroom on top, not a token amount. Whatever the card manufacturer recommends is a reasonable floor and they set it with transients in mind.

Buy the higher of that and your own arithmetic.

Two things that are not reasons to go bigger: future upgrades you may never make, and the idea that a bigger supply is inherently safer. And one thing that is: a supply loaded at a moderate fraction of its capacity runs cooler, quieter and usually more efficiently, which is a real quality-of-life difference.

So your 850 is not wrong. Where the cheap-and-large instinct fails is the next answer.

The price difference is largely real, and the efficiency badge is not the thing that varies.

That badge measures efficiency, how much comes out relative to what goes in. It says nothing about voltage stability under load, ripple, the quality of the capacitors, the protections, or whether it will fail gracefully. Two units with the same badge can be very different products, and this is why the badge misleads so many buyers.

What you are paying for at the higher end:

Stable voltage under transient load, which is exactly the shutdown problem above.

Proper protection circuitry, over-current, over-voltage, short circuit: that actually works rather than being listed.

Better components, particularly capacitors, which is most of why one lasts a decade and another dies in three years.

A longer warranty, which is a decent proxy because the manufacturer is pricing their own failure rate.

The practical approach: find out who actually manufactures the unit, since a relatively small number of factories build supplies for many brands, and look for an independent review that measured it on a bench rather than a written overview. A well-reviewed mid-price unit is the sweet spot; the very cheapest tier is where the corners are cut.

The reason this is the one component not to economise on: it is the only part that can take the others with it when it fails.

Most components fail by stopping. A power supply can fail by delivering the wrong voltage to everything connected to it. That is uncommon and it is not theoretical, and the cheapest units are where the protections that prevent it are thinnest.

It is also the component you keep longest. Graphics cards and drives get replaced; a good supply survives two or three builds, which changes the arithmetic on paying more.

A few practical notes for the purchase:

Use the cables that came with the unit. Modular cables are not interchangeable between brands or even between models, and using the wrong one is a genuine way to damage things.

Check the connectors your card needs, particularly if it uses one of the newer high-power connectors, and make sure the supply provides it natively rather than through an adapter.

Do not reuse an old supply in a new build to save money. It is the part that has aged the most and it is now under a load it was not sized for.

On your instinct: big is fine, cheap is where the risk is. Buy the wattage you calculated, from a unit somebody has actually tested.