For a system with loudspeakers you need as a minimum:

• A music source. That may be a CD/DVD or a music data-file. The music data-file may be in an uncompressed format (FLAC) as the best or in a compressed format (typically MP3), which is often sufficient. The "old" CD standard is based on 16 bit sampling at 44.1KHz and on the limit of not being seen as audiophile today. Data-files sampled according to better levels can be found on the Internet.
• A sound reproduction unit that can generated analog sound signals from the digital information on the CD/DVD or in the music data-file. A good CD/DVD player is not cheap because you need one with a good signal processor and a high quality DAC (Digital to Analog Converter). Good reproduction of music data-files can be achieved at a moderate cost with a smart-phone or laptop computer and a separate DAC that accepts a USB input or an optical Toslink input.
• A volume control, that in its simplest form is a potentiometer or an attenuator. The volume control may be part of a simple low distortion pre-amplifier with a low impedance output. A high quality headphone amplifier may eventually be used as volume control. Tone-control or equalizers are normally not needed in audiophile systems where they often are source of unwanted distortion.
• A power amplifier, eventually as describes on this site. Class D or class AB.
• Loudspeakers of good quality. They may be made DIY if you are good with wood-work and know suited speaker units. Else, it is suggested to buy them on sale with typically large discounts. The loudspeaker manufacturers have got equipment to manufacture loudspeaker cabinets at very low cost and they buy the speaker units with huge discounts compared to the price you have to pay.

For a moderate cost system it is proposed to use music data-files (preferably in FLAC format) on your smart-phone or laptop, streaming the information to an external DAC (eventually using Bluetooth) and then send the analog signal through the power amplifier to the loudspeakers.

You probably have a smart-phone or a laptop already. The DAC should be at least 24 bit and able to handle a sampling-rate of at least 96KHz. Such can be found from around 40 EUR and upwards. The better ones have an optical input (Toslink) as well as a USB input. You may even buy a DAC with a Bluetooth input that accepts the aptX protocol. Building an external DAC from scratch yourself is a lot of work and typically without performance gains or savings. The power amplifier with a volume control is ideal for DIY and inspiration may be found in these pages. The loudspeakers should, as it has been repeated for decades, be where you invest most of your money. Poor loudspeakers always leave a poor system. The speaker cables should be of good quality with a large cross-section without being excessive.
Excluding the smart-phone or laptop, such a system can be made for 300-600 EUR and it will perform much better than most fully commercial systems at higher costs.

One statement will be made here: It is much more important that a system sounds good and has a low distortion (Total Harmonic Distortion / THD) than it is particularly powerful (Watt). Just 10 Watt will do for most daily listening and 20-50 Watt will normally do in your living room.

For dance parties or public address purposes more hundred Watts may be needed but the quality is less important. Borough a party amplifier when you need it. Be aware that excessive sound levels may damage your hearing for the future and limit your abilities as an audiophile.
High quality sound is much more relaxing than dull sound and you may start appreciating even other kind of music than what you used to listen to.
Also, remember there is a limit in the human physiology. Differences between music with 0.01% distortion and 0.0001% distortion is only possible to hear for very trained ears. Often the loudspeakers set the limit anyway. You can spend thousands and even ten thousands on a system and your gains in sound quality are not correspondingly large. Most of us have moderate means and this is why the focus here is on how to get most out of a limited budget.
Audiophile sound is subjective and often characterized by a "transparent" sound where you can hear all instruments playing better and where details, like breathing of the singer, can be noticed. Sometimes such sound is described as “analytic”. An audiophile music system must be able to handle even deep bass well, but not with an unnatural level. The bass must be well controlled and die-out naturally (fast) such as it is the case with the sound from a bass drum.
Far more competent audiophiles than us can tell you more about what to appreciate from a high quality sound system.

As power supply for the power amplifier you can, at least for a start, often use a power adapter of the type typically used for laptops. For amplifiers with a single supply voltage a standard 19V/90W adapter will in many cases do fine with some extra decoupling capacitors (4700uF-10000uF/35V) connected at the output. Even better are 12V-24V adjustable 96 Watt adapters where you can vary the supply voltage according to the amplifier.

Money can be saved by re-use of certain components from elder amplifiers or receivers that are due for being trashed. The power transformer and eventually the large electrolytic power-line decoupling capacitors are often worth saving. Heat-sinks, some connectors and good quality potentiometers as well. In the past components were often manufactured with a higher quality (and price) than today and deserve a second life. Elder, high quality DAC's (external) have with success been re-worked to include modern OP-AMP's.