Thinking of simplicity, would you consider an all-in-one solution (active speaker + DAC + streamer), such as KEF's LSX Wireless ($1400 retail) or KEF LS50 Wireless (as low as $2K at Accessories for Less, so above your initial budget)? If I were going for the simplest implementation, I'd look strongly at the LS50s, since that gets you a great speaker for the long term with amplification, DSP, DAC and streaming. ELAC's streaming speakers may also be an option -- I just am not familiar with them.
If you prefer to use a few more components -- for flexibility or your particular set up -- I'd focus on the passive speakers first, as others have suggested, then get a Chromecast Audio dongle off eBay and run it to one of the lower-cost but high measuring DACs reviewed here, from SMSL or Topping, choosing one with volume control. Then I'd run that DAC/digital Preamp to whatever decent amp you can find, either something reviewed here or a used one bought locally ... many people have old amps they can even offer. The amp will depend on the speakers you go for (in turn dependent on your room and listening interests), and you'll get good amp advice here once you have speakers selected.
And if you want components but simpler still, look at a Denon or NAD integrated amp that has streaming and ethernet connections. This would be my last choice (having done it), because the DAC won't measure as well as the separates route, but it will still offer great sound -- and it will be easy -- just add speakers and you're set. But if you go this route, be sure the integrated amp a) has network connections and b) can use streaming software that's decent, such as Roon. I'd recommend Yamaha except they do NOT give you access to good streaming software, and you're locked into their crappy Musiccast interface.
Final thought: Speakers first, yes, but music interface is also really important. You'll spend a lot of time with the interface: Roon, JRiver, Sonos, Heos, etc. You want to invest in something that's a joy to use. Roon is great -- and I strongly suggest you pursue a solution that allows you to use Roon, or at a minimum your preferred streaming services (Amazon, Qobuz, Spotify etc.).