What is proper ratio of money spent on amp/preamp/integrated vs speakers? 1:1?

"Still, more power never hurts."
Perhaps. There are examples of higher power amps from the same manufacturer's line that just sound worse with some speakers. 
Then I think of the old Crown DC300's we used to sell, compared to the "lesser" DC150's. The 150's sounded better with every speaker we paired to.
As they say, "It depends."

An earlier comment mentioning "trophy systems" was a great phrase. It's often torture when "invited" to hear the latest trophy.

But my pet peeve is phase shift, and many fancy systems just cause too many detrimental phase interactions.
That's less dollar-related.

Long time ago, I was told that it should be half of the budget for speakers and half for everything else. I am sure it is far from solidified truth, but have had hard time not calculating it in the back of my mind.

At that time, "everything else" was a record player and an amplifier, maybe a cassette player, too. All this trickery with cables and room treatments was not on the radar quite yet. I am not saying it is not important, but it was not part of the equation when I was told the secret formula.

Free speakers! That’s the solution! And my wife would be so much happier too!

Wife happier with no speakers.Or maybe invisible speakers.

eddie,  you will get a million answers go out
spend as much money as you can   forget about it 
 you will go nuts trying to
have fun   

@tlinkie, yes white  speakers, white background goes down really well. Helps with imagery a bit too.

As for this magical ratio, well as @mikapen said sometimes spending more = worse sound. Not all companies are like Harbeth or ATC where spending more gives a better sound. Far from it, especially for amps/cables etc. But we all know that, don't we?

Again, it all depends upon at which price point you can hear the performance flat lining.

You might have to discover where the sweet spot in a particular range might be, or else risk being forced out of your listening room by the sheer number of boxes which have almost surreptitiously taken up residence.

I have a friend whose front room looks like he's installed a console from Cape Canaveral. Seriously, reconnecting or rewiring his receiver is a two man half day job.