How much does power amplifier really matter comparing to other hi-fi components?

Assuming a budget of $10K-$15K, I might put nearly everything into a pair of JansZen Valentina A8 active speakers. Plus as little as $550 for a Bluesound Node (the source) and < $100 for cables.  Then trade up from the Node later (to Bryston/Cambridge Edge/Exasound).  That's assuming I lived within reasonable driving distance of the JansZen shop in Ohio (otherwise, I'd be reluctant to put all my component eggs into their basket).

But suppose a $5K budget instead, as a more reasonable entry point for a "high end" clean slate system. Assume we're going for digital not vinyl. Then very roughly:
1. 60% for speakers (because they make a bigger difference than anything else and are a little harder to trade up due to size/weight);
2. ~10% for a streamer/DAC (such as the Bluesound Node);
3. 30% for an integrated amp (maybe Peachtree or Cambridge Audio);
4. very little on cables (Bluejeans Cable for speaker wire; for everything else, just use what comes in the boxes with your components for now.)

For half that budget, you could build around a pair of KEF LS50 active speakers ~$1250) plus < $1K for everything else, with change back.

As between pre- and power-amp, it's really a question of what kind of sound you like (warm, analytical, bassy, slightly rounded edges, etc.) and then carefully matching components, within your budget, to get that sound. You can combine a relatively expensive power amp that has a sound you like with a passive or very clean active power amp that is not very expensive. Or, you can spend more on a pre-amp that gives you the sound you like and less on a power amp that adds nothing but power to the sound. Personally, I'd rather have a pre-amp determining the sound and a very neutral power amp. These days I run a Parasound JC2 preamp ($4500 when not on sale) with a pair of VTV Purifi 1ET400A mono blocks (about $2000). Some folks prefer combining tube or hybrid preamps with solid state power amps. But instead of adding the distortion of tubes, I've just ordered a Schiit Lokius tone controller ($300), which allows me to tailor the sound to the peculiarities of specific recordings.

     Every component shares a slice of responsibility, when it comes to accurate sound reproduction (not to mention: room treatment).

     ie: Picture all of your components (sources, cables, pre/power amps and speakers) as panes of glass, through which you want to observe something living.

      The accuracy/enjoyment of your observations will be determined by how many and how dirty the panes.

       How critical you are as listener, will determine your level of involvement and investment.

I believe it’s a good percentage of your system and should be chosen per your speakers and their capacity. Don’t forget your power conditioner and monitor. I spent 500$ on one that insures it’s protection. 

Everything matters. Amp matters a lot. Recently I’ve owned 3 amps I can swap among in my system. Each has a very distinct sound. All 3 are way more than enough power (120 - 275 Watts / ch) for my 96dB Tannoys, so overhead & drive capabilities are not really a variable. I’m even writing down particular combinations of cartridge & amp that work best together lol.