I spent a good few years going through many DAC's, aiming for an improvement in CD replay each time. I finally started getting where I wanted to be once I tried Theta DACs, which kept me happy enough for a few years until I discovered the Monarchy Audio M22 series. They blew away everything I'd tried or heard up to that point. I now stick with an M22B and also an M22C and no longer feel a need to experiment further as the sound quality is amazing.
Different CD players do sound different, even when using them as transports as I do. I own four, which I am happy with.
I tried Toslink optical connections many times, but ended up concluding that SPDIF digital coax (digital phono lead) was superior, although many leads of either type are not up to much. I now make my own digital phono cables specifically for CD to DAC use, which I find superior to most and as good as any (in other words, extemely good).
I have a few of these cables in 0.8m length and may consider loaning one to established UK members to try if interested.
It is impossible for anything digital to sound analogue, because it isn't analogue!