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

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

Understood.

50+ years in audio and I know only 3 things(slow learner) .
NEVER buy a preamp without a gain switch or nob and a TT without
a fly on the play adjustment .
That and  impedance matching IMO will solve 90% of 'too harsh, no base,etc.etc. etc. etc. etc. etc , complaints on here or anywhere else for that matter .
And you can buy 3 cars with the money you save or pay your daughters way through the local state university . And buy her a new car upon graduation .

It's the riddle for which there is no answer, the corollary to "not all things that can be measured count and not all things that count can be measured". System dependent, but in many cases, a great preamp creates the "jump factor" that turns a boring system into an attention grabber. That's a fact. Debate it all you want.