My last rodeo

I was in your position about five years ago, with equipment I had purchased in the 1970s through 1992, after a flooded truck ruined my Infinity RSIIb speakers.  I started out in 2020 to buy a pair of speakers in the $5K range, but after hearing the Fyne F-702s and getting concurrence from my better half, I bought them; unfortunately, their price has increased significantly since I purchased them, but the F502SPs may give similar results, as Fyne says they have incorporated features the F-700 series in the F-502SPs..  I find their imaging, tonal qualities, and overall musicality to be excellent, their only shortfall was in the bass region--8" bass units-so I added two Rythmik F12SE subwoofers that significantly improve all aspects of the music. I have a Rogue tube preamp and finally settled on solid state mono bloc amplifiers, although a single stereo amp might do equally as well.  I finished the primary music chain with Silversmith Fidelium speaker cables, which had an impact FAR beyond what I expected in sound quality. The only legacy pieces in my system are my NAD C658 CD player, used as a transport into my Schiit Gungnir 2 DAC, and my Thorens TD 126 MKII turntable with Audio Technica 540ML cartridge feeding into a Lounge Audio phono preamp.  I have on order an Innuos Stream 1 with linear power supply and the Phoenix USB reclocking output board.  Not counting my legacy equipment which was about $1100 in much older and more valuable money, my current investigate over the past four to five years is almost exactly your target amount. Were you to go with something like the F-502SPs--made in Scotland--and a stereo power amplifier, you could probably build a very decent system for a good bit below your target price.  BUT, as I am sure you are fully aware, you must listen to speakers to determine whether or not you like the character of their sound quality.  That would be the first step, as it was for me that sent me down this path to extremely satisfying listening.  Best wishes in your efforts.