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

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. 

System dependent, but in many cases, a great preamp creates the "jump factor" that turns a boring system into an attention grabber.

+1 @fsonicsmith 

"System dependent, but in many cases, a great preamp creates the "jump factor" that turns a boring system into an attention grabber".

True it can wake up a boring system ,but it can also make a system too alive and strident