How much do I need to spend to get a preamp that sounds better than no preamp?

Hard wired tone controls.

I agree about integrated amps. I have the new PassLabs INT-250
and an OPPO MODWRIGHT 205. I doubt that I could get better sound from separates. To me if you have good speakers and an
excellent amp, the input sources become the most important issue.
Each time I have improved one, the system improves considerably.

By the way fo those of you with MODWRIGHT OPPO's the tube
quality is critical to its performance. Ask Mod Wright which tubes they use at shows. I did, changed to Philips and Amperex and transformed the OPPO into something close to vinyl.

Lots of chatter lately about the pre or not to pre debate. I tried the direct source to amp route and was immediately impressed by the increased level of detail. After listening to it like this for about a month the music started sounding dull and lifeless. Put a Schiit Saga passive pre in with it's hybrid tube buffer and stepped attenuator and it helped a bit. I think I'm going back to an active pre, still feels like I'm missing something. 

Unless you get a quality tube preamp then there should be little difference from adding an SS preamp in the path. A quality tube preamp will not necessarily be transparent but good ones will give you a wonderful warm presentation. Keeping signal levels as high as possible without clipping can be extremely important to get the most out of a preamp.

Honashagen 4-22-2018
No balanced inputs on my DNA1.

I’m not sure from this response if my suggestion came across clearly. To be sure it’s clear, I was suggesting that you consider **adding** balanced inputs to the DNA-1, either with an external Jensen transformer or via the mod Steve McCormack had offered, and perhaps still offers. I suspect that doing so would allow you to utilize better sounding outputs of the BDP-105. It would also eliminate the possibility that ground loop issues between the player and the component it is driving are affecting sonics.

A potential benefit of using the external transformer approach, rather than Steve’s mod, is that it would provide you with the flexibility of having the Audible Illusions preamp (or some other single-ended preamp) either in or out of the path, while using the balanced outputs of the player.

Regards,
-- Al