I can very confidently recommend the Mission 778X amplifier. £549 buys you a flexible amp, with built-in DAC, phono stage and headphone amp that are all excellent, and it's all nicely screwed together as well. At present, if you want to keep things compact, the Pro-ject CD Box E can be found for £199. It's tiny, and best suited if you tend to play a CD all the way through rather than skipping between tracks, but it sounds excellent.
Less quirky in operation is the Audiolab 6000CDT, but that's a lot more money and a transport only - no hassle seeing as it could be connected to either the optical or coaxial input of the Mission. You could get the CDT paired with the Audiolab 6000A amp (either one of the last of the outgoing model, or the new MkII), and that is also an excellent combination. If you fancy a bit of retro, the Leak Stereo 130 and CDT are also excellent, and share a lot of parts in common with the Mission and Audiolab components (all are made by IAG). In short, it's hard to go wrong with any of the IAG products around this price.
Any of these options leaves you with ample to choose some speakers. I've kept coming back to Dali over the years, and can warmly recommend any of the current Oberon range. With either the Mission or Audiolab amp, there is enough neutrality and sufficient grip to work with a good range of different speakers, so it's worth doing lots of research on this part of the system. I'd be cautious with KEF (I've listened to the Q3 Meta and the Q Concerto Meta and was very disappointed), and ELAC (I had the Debut 3.0 DB6.3 and could best describe them as a bit of a wet fish), but there's loads to consider from the likes of Fyne Audio, Monitor Audio, Mission, Wharfedale, Dynaudio...
If you fancy adding streaming, you could go as simple as a WiiM Mini, find a middle path with a WiiM Pro Plus or Ultra, or go for something like the Eversolo DMP-A6gen2 or Bluesound Node Icon. To be frank, I have the Eversolo and a WiiM Ultra here, and although it has some advantages (principally a better screen), the former doesn't justify being more than twice the price of the WiiM.