A primary question has to be how far do you want to go with sound quality? I.e. do you want to just get some streaming ability or now even if maybe not up to the rest of your system, or do you want to match the rest of your system, then have done with it, or will you be wanting to upgrade other things as well in due course? What best depends on these considerations as well as, vitally, available funds, as judicious steps can save a lot of money over rime, and of course always consider buying secondhand if money is tight. Also, whilst you see streaming as a secondary or tertiary source now, one day your CD player will fail, being mechanical - if in the meantime you were to rip your CDs, and if your streamer is good enough, you could have same or potentially better sound quality, and wouldn't then have to replace the CD player.
As Hal asked, one consideration is where you presently keep any music files, or anticipate in the near future. If on a PC, there are various inexpensive programs available that will play quite well (others will have to advise as I have no experience), and depending on your CD player you might be able to feed into its DAC, getting you going for next to nothing, to maybe add a better DAC later. BUT computers are bad electrical environments as far as sound quality is concerned, so optical connection would be best if using the computer's own audio output, but probably better using usb output with an isolator/convertor between it and the DAC unless the latter has galvanic isolation and rf filtering (many don't). The Gustard U12, costing ~£120 new, is one that is very effective. If on a Mac, the same considerations apply, but I can recommend Audirvana as an excellent rendering app that is capable of matching or exceeding the SQ of your present system, depending how set up. If you don't yet have a music store, I can recommend the Mac Mini, best is 'late 2012' model, which is readily optimised for best SQ and once set up can be run like any hifi device, just turn on and go, while it gives a platform that stands up well to stiff competition (more on other threads).
If your CD player doesn't have a digital input to use its DAC, then a stand alone one would be needed for decent SQ. the Chord Hugo punches way above its weight, and should easily get the best out of your system if coupled with something like Audirvana and an isolator, while still having more to offer if you might some time upgrade the rest of your system, but even s/h may be out of budget. Some people say its little brother, Mojo, is good, while a number of people on these forums have appliauded the Audioquest Dragonfly DAC, which is extremely cheap - I can't comment on either as I've never heard, but may be worth researching.