High end stuff has no limits, there's always a better system in some feature/property. Also, when you start to upgrade something, there's chance of endless loops (these speakers needs better amps, which shows some defects of my DAC, etc.)
So setting a limit, reaching it and leaving it there is good IMHO.
I run an entry level HiFi CD player with iPod interface through a vintage amplifier to a pair of bookshelf style speakers (which are pretty big for their class though).
If my friend is confusing whether his phone is ringing because a similar sound is present in the playing track, then it's good enough. Similarly, if you're enjoying the sound you're getting from your system, you've accomplished your goal IMHO.
I'm neither looking for loudness, nor for that ethereal sound. If I can hear everything in relatively clear manner, and I'm enjoying it, that's it. I'd rather enjoy it instead of sweating over smallest details.
Lots and lots of variations. But basically get a $250-350 pair of speakers for a decent brand (Dali Spektor 1 or 2 are a good bet) and plug them into a $100-200 second hand amp and you've got a great set up. If you don't want to go second hand then Yamaha and Sony have some decent amps in this price range.
Spend whatever you have left over on a second hand CD player or DAC for your phone, depending on what you want to use as a source.
JBL 305 + 310S matching subwoofer will measure impeccably and play nearly full range with strong bass down to 27ish hz. Would have to catch some sale prices around black friday or some such.
Or this excellent DIY kit and basically, any solid 50-100W ish amp. Might push you up to more like $600. But you get the idea.
I have a generally very high opinion of Wirecutter's bookshelf speaker and receiver recommendations - any recommended receiver and any recommended bookshelf speaker, basically. Although, most retail bookshelf speakers in this range might be more like an 80% experience not 90% lol.
Another thing you can do for a very legitimate hi fi experience on a budget is to turn modest speakers into excellent performers with DSP EQ. Either automatically with a receiver that has e.g. Audyssey auto correction or with a MiniDSP etc.
Audio reproduction is, well, signal reproduction/amplification. Whether a driver produces objectively correct sound via excellence in physical driver construction and engineering, or via a DSP assist, makes little difference.
Mine is a bit more expensive, since I bought the speakers new (I had somewhat specific demands), but everything else was second-hand.
I've got a pair of Monitor Audio Bronze 2s, a Denon AVR-1911 receiver and two Dali SWA 12 subwoofers.
As I wrote above, I bought the speakers new, because I wanted relatively large bookshelf speakers with front ports and living room-friendly looks, and nothing presented itself second-hand. With a bit of patience, you should be able to find a solid pair of speakers in mint condition for $2-300, no problem.
The receiver has 90W per channel (for real, no tricks), Audyssey room correction and was just $80 second hand from a guy who had upgraded to a 4K-capable receiver. I have it hooked up to my TV and so on, but at that price I would be perfectly happy just using it as a stereo amp, since it has good power, digital inputs, room correction and bass management for subwoofers.
The subwoofers were ~$200 each second hand, years and years ago. I'm sure they're even less expensive now, or you can just do without subs.
I also use HifiBerry's AMP2 to drive a pair of old Kenwood speakers with a dedicated subwoofer (it's a 2.1 set out of the box), and boy, that thing's impressive for its size.
It has a Burr Brown DAC and a Class D 2x30W amplifier on board. It has delicious sound.
You'll probably want an interface that has TRS/XLR outputs instead of RCA unless you want to get a weird cable. Focusrite Scarlett Solo would do the trick nicely!
I strongly believe a really good "90% of the way there" system can be put together for well under $500 retail, or even less if going DIY or used.