DVD player playing CD's

The DVD player should be better. If you look at the error rate coming off a CD player data stream, much higher than a DVD player. and remember few of the high end CD players make their own drives, almost all sourced from China or Japan. the Real question is what DAC will you use with it?

We have a SONY DVD/CD unit.  The only complaint is it only takes one CD at a time but it truly sounds just fine.  Multi-unit CD players or juke boxes are more convenient.

Good luck. Just use the best cables you can afford or if it has an optical out for Audio alone.
Some units only have one optical out.

My Parasound Hilo has two optical in's and one is used for a standard CD changer and one for TV Dish audio.

The DVD/CD player is in another room not our main system but works well.

It really depends on the player.  I have a Rotel CD player that listed for around $1000.  I have a OPPO 95 DVD-BluRay player that also listed for around $1000.  I think the OPPO sounds better playing CD's that the Rotel does, plus it plays SACD's and DVD Audio discs.
You really just need to do a little research on the different players and then bring some home to audition them in your own system.

I use a Multiple Format Digital Disc player, it's a Esoteric DV-50. It's pre Blu-ray but it plays most everything else.

The thing about DVD players is, depending on the unit, there might be a brief pause between tracks. With some CDs this can be annoying. But other than that I would expect a DVD player to work fine playing a CD.