I’m going to try and give you insight on these things.
Before you go out and buy anything, are you listening to .mp3s , .wav files (CD quality) or .flac ? If you are listening to lossy music (rather than lossless) the entire premise of achieving better sound quality is meaningless. Since with .mp3s there is information that is omitted or missing, the kbps data rate is only up to 320, vs 1411 for CDs, and even higher for high-res. I listen to redbook (16 bit by 44.1 KHz CD rips)
Bluetooth - I think we’re at version 5.0 now.
The purpose of a headphone amplifier is to optimize the driver modeling behavior of the miniature driver units that produce sound in headphones. A more dispersed pattern of even pistonic movement is achieved with a headphone amp, or any 6.3mm port that is dedicated for that purpose. And obviously, the purpose of an amplifier (headphone amp in this case) is to enhance the strength and integrity of the input signal (your source component).
Computer sound cards are okay. Check out ASUS xonar USB DACs and PCI-e sound cards. Both are great value for the money...You can upgrade as you go...feel free to message me if you need more clarity.