I will add my few cents worth.
Speakers are I think the best area were devoting more funds will generally improve results. However you have to be careful. I have heard more than a few very costly speakers that were really dreadful. So the cost benefit ratio has a huge scatter.
In bad rooms, treatments can help. In my view most rooms do not need it, and it is an area were expenditures in this area can make things worse. In addition a lot of spaces do not lend themselves to acoustic treatment. Speakers have an impact here. Most room problems are in the lower octaves. As I have frequently pointed out, low Q speaker designs will minimize these problems and high Q ones exacerbate them.
When it comes to turntables and analog tape recorders, then increased price with close tolerance precision engineering pays huge dividends including sonic performance and long life. However I think you have to beware of modern turntables with high prices catering to the audiophools. Many of these turntables spend huge amounts of money trying to solve minor and even non problems to exclusion of an overall satisfying design. In my view the modern trend in very high priced turntables to high mass arms and lower compliance cartridges is plain wrong. Good high priced vintage turntables if chosen carefully are more often than not very rewarding.
Electronics is a difficult area. I don't believe there is a strict price performance trend. I do not believe all amps sound the same. You have to choose wisely. It helps to become familiar with amplifier topology. I think the design has the biggest impact, on quality and reliability.
The most difficult projection to make is reliability and this is all over the map. Some modest designs can have long legs, and more than a few fussy, costly and exotic designs have really been in need of a chimney!
Most digital devices like CD players for instance have become utilitarian. When assessing purely digital performance I'm not persuaded you can tell a cheap off the shelf player from an exotic.
Often not mentioned is steaming digital material. Here I think at least time and trouble pay huge dividends.
I have had a big focus on this technology for a little over three years now. It is clear from the BBC that encoders are not created equal, and customization is required. This also applies to the receiver end. I'm certain that off the shelf devices provide far from the best quality available. In this area significant DIY is currently required and not insignificant expense. It is how ever a very rewarding area to become interested in.