I've found that budget wise, running your computer into a decent DAC is the way to go. To beat it with a CD Player you'd have to go up pretty significantly in price. This is not a rule though, just an observation from MY experience. MY experience also has shown me that old CAL CD Players on the used market are a real steal for the price and are hard to beat on a budget.
As I do not want to be tied to the location of my computers -- desktop or laptop -- I run my semi-portable Headroom Micro dac from the digital coaxial out on either a basic Toshiba DVD player or a portable AG DVD player, depending on which of my residential listening locations I happen to currently be in. I find the quality of listening through either my Little Dot MKII or Bottlehead S.E.X. amps to be quite good.