I'd always suggest used over new. It highly depends on your listening preferences. For a grand, you should be able to get:
Audio Research CD-2
Audio Research Dac 1, 2, or maybe even 3
Theta Gen Va dac (highly overlooked these days, originally sold for $5k)
Theta Miles
Mark Levinson No. 36
Lector CDP .6T
Timbre TT-1 dac
Audio Note dac 1.1x
Cary 303 or 302 I forget the exact model number
BAT VK-D5 if you get lucky, I have seen these go for below a grand although very seldom
There are others, but those are the ones I liked the most in your price range.
Others worthy of consideration but I have no personal experience with:
Opera Consonance CD-120 Linear
Jolida JD-100A
Shanling T100
Right now, I'm living with a Marantz DV9500. But prior to that I was using an mbl 1511D (originally sold for $10k). Next month I'm planning on acquiring an Ayon CD-3.
Let's get my definition of a giant killer out of the way first. IMO a giant killer is a component which costs less than but can compete or sound better than the reference level stuff. I would consider reference level equipment to be $2k+ used market prices for recent models and $1k+ for older models. Also IMO, reference level equipment should approach the sound quality of a good turn table or even live music. I have encountered a few giant killers, but all of them were more than a grand on the used market. Reference level equipment can differ in sound. But IMO they all have a certain refinement to the sound which lesser equipment just can't touch.
When I heard the stock Oppo, I was highly disappointed given all the rave reviews. IMO it is mechanical sounding, somewhat analytical, dry, lacks in spacial cues, and not very engaging. However, I did get the chance to listen to a highly modded Oppo and again IMO that can certainly be considered a giant killer.