Relative component value to overall SQ.

@douglas_schroeder +1, a step above dead on arrival. : )

@n80 There are true gems of posts in this thread. There is nothing "obtuse" or a "hem or haw" about them. I appreciate your appreciation of the replies.

Simply giving the OP what they asked for. Not questioning why they asked for it.

Not as many B & M stores to hang around listening to different types and prices of speakers , amps etc.. as when I started out, actually there is only 1 left within about an hour and half drive from where I live now so it’s a little harder to build relationships and get good advice not to mention good deals on returns, trade ins and demos from a dealer. At amy rate I always thought the speaker is where most effort and money should be focused but at the moment I am doing a home trial of a set of speakers that cost less than my integrated amp so what do I know? Staying in the parameters I would still put speaker at about 55%( he or she can figure room treatments out later maybe do some home made things) , amplification either separate or integrated close 44% and the remaining 1% on cables. But the more I read the better I understand I’m not an audiophile just someone who likes to listen to music on the best I can afford which is pretty modest from what I can gather.

The speaker-room interaction is the most important, but that does not necessarily mean it will cost the most. A small listening room with nasty bass nodes may benefit from a small stand mounted speaker/monitor considerably cheaper than a speaker required to fill a larger more neutral room. So I agree that it is so difficult to generalise.

Also to a newbie I would seriously recommend looking at active speakers with built-in amplification. Then simply add a source/pre-amp combo.
The ATC room at Munich had their £3k cd/DAC/pre playing into their active speakers and it sounded a dream - a one box solution with 80% of the cost being on the speaker. Definitely worth considering for a first-timer.

What I don’t understand is why the OP would ignore the source? Are you assuming all sources are equal?You can’t assume a perfect signal from any source. In the 1990s in the UK the general advice was to spend 50% on the source. These days I rarely hear that but nevertheless I would recommend certainly spending as much on the source as on amplification.

In summary, and with caveats explained in the first paragraph, I would say to a new Hi-Fi enthusiast seeking advice:

Trad system
Single source (including DAC): 20%
integrated amp: 20%
speakers: 50%
cables/rack/isolators: 10%

active system
source/dac/pre amp combo: 25%
active speakers: 65%
cables/rack/isolators: 10%

If affordable and within the budget active speakers with dsp or a preamp with dsp would help solve room issues without treatment. And treatment is demanding on your space in terms of size (bass traps) and decor, so dsp would be easier for a new hifi enthusiast to deal with.