If you are new to this, it is important to understand the different parts of the process, and associated terminology. Playing from stored music files involves the store (e.g NAS or computer hard drive), rendering software (‘renderer’), yours presently being something installed in your computer, whether part if the standard laptop package or something you have installed (do you know what you use?), and a DAC, feeding an analog signal to amplification and speakers.
The three stages before amplification can be in separate boxes, or commonly the renderer and DAC combined, commonly called a ‘streamer’, or the renderer and store combined (as in your computer), variously referred to as ‘player’ or ‘transport’, or all in one.
A NAS as a store, addressing your specific question, as others have indicated need not beparticularly expensive, well withing your budget for something very good - and you can do for less without compromise to sound quality, (though my experience of a cheap NAS was intrusive noise from its fan, something to be aware of, whereas, for example, QNAP has no fan). However, you need something to do the rendering (converting the file to a digital music stream), which NASs don’t do - your computer could do that as it does now with online streaming, but if you have to have the computer running for playing music, you might as well store the music on it if capacity is enough, or an attached hard drive, rather than a NAS. If you don’t want the laptop running to play music then something else has to do the rendering, and keeping within your budget for NAS and a renderer starts to get more challenging.
Incidentally, in terms of sound quality a significant component is the DAC. It may be helpful for people making suggestions to identify what DAC you use.
And in terms of storage capacity, how many albums do you envisage? (Is it transferring (ripping) a an existing CD collection to hard drive storage, or for future purchases?) it is significant to the size of drive you need, whether in NAS or a computer. I have about 1200 albums at CD or higher resolution in lossless format (.flac), with some space to spare on a 1TB drive - I consider it quite a large collection, but some people have far more.
Also worth bearing in mind is that provision of another drive external to, and removeable from, the NAS or computer to use for backups is wise, at least unless you have all the music stored on CDs.
What you will find from people’s responses is likely to come from a variety of backgrounds and experiences, so be prepared for sometimes apparently contrary opinions and likely confusing options, and give yourself time to pick through it all before making a decision. As has been suggested the advice of a dealer can be valuable, if that is practicable.
I switched to streaming when my CD player needed replacing, seeing it as the medium of the future, and whilst with hindsight and improved knowledge I could have made better choices in terms of value for money at first, I have never regretted it in the slightest.