DAC/w Volume control + Power amp or DAC + Integrated?

Built in volume control affects sound quality of the DAC?

No they are better, if not used too low down.

I use an MSB discrete dac with volume direct into monoblock poweramps, and the sound has never been better.
But if you have to use the dacs volume below 2/3rd because it’s too loud, you will start to slowly loose resolution (bit strip) depending on how low you go.

The answer to fix this problem insert a $49 Schiit Sys passive between the dac and poweramp/s and preset the volume on it. so then you can use the dac’s volume above 2/3rd
https://www.schiit.com/products/sys

This way you’ll get better poweramp/s for the same money as an integrated and also save big on not having a preamp if you were going separates.

Then some good dac manufacturers like Wadia have thought about everything so you don’t need the Schiit Sys, in using a volume control in dacs only up high for maximum sound quality in all systems, as they have gain links inside so you match it to your system gain and use the volume only in the top 1/3rd of full up, as you can see from the setup instructions when you get it. (Read the paragraph that starts "Premium sonic performance is achieved")
https://ibb.co/JQJMx8S

Cheers George

It really depends on the DAC.  I had a PS Audio DSD which is an awesome DAC but the volume control in it is not strong.  There are a couple reasons for this, but it was inferior to my preamps.  

I have since moved to Chord and Rockna DACs and the volume control in them is completely different.  Right now, going direct from the Hugo 2 or Wavelight into my amps from DAC is dramatically better than the Schiit preamp I currently have in the system.  

An LTA Ultralinear with a Chord Hugo 2 would easily be on budget and will sound amazing.  

That being said, the UL integrated is not even close to inferior.  The line stage in it is tremendous and the volume control is a superb R2R.  An Ultralinear Integrated with a DAC like the Chord Qutest which would be brilliant.  

In both cases, we could definitely keep you on budget for new gear. 

If using a DAC with volume control I would want one where it was in the analog output stage. 

Another approach would be a passive pre between Dac and amp. If using a DAC with tube output stage into a tube amplifier one has plenty of tube driven gain. 
One can find tube amplifiers that have variable input gain to better control system gain. The maker of my presmp, Aric Audio, makes tube amplifiers that have this such that one can run a fixed gain DAC directly into the amp. His amps have 6SN7 tibes in the input and driver stages. 

@Jiss Sorry to bother you. Ye I did read a lot of discussions but my question was more related to cost savings. 

I was looking for significant savings over going Integrated.