Spend only $250 for a used DAC? Geez, how horrible that will be! And in a system of otherwise fairly decent performing products? NOT! You're pushing your luck to find any DAC, new or used, for less than $500, and probably closer to $1000, that will have any chance to bring the music to any level of reality that you would expect the other components to achieve. Spend more on the DAC and look for a good deal on a used CDP for $100-200. The difference between DACs is magnitudes greater than the difference between transports.
And $3000 for an integrated? What? A top performing line stage from ARC (LS5), CJ (Premier 10/14), BAT (VK5) from 10-15 years ago, can be had in the $1000-1500 range that if matched to a SS amp from the same company or others like from McCormack, would easily be less than $3k and pretty much destroy any $3k integrated amp. And you'd have $500 or so extra to get a better DAC.
There are so many phenomenal speakers under the $2k range that for an $8k system, I think you will be mightily impressed. No need to spend more at this point.
I'm a huge proponent in putting top-tier cables in a system, but I'd start with DIY or low-cost speaker cables and stock power cords. The only exception would be to invest a few hundred for an IC between the line stage and amp where it makes a major difference with line stages like the ones I mentioned.