How important is the pre-amp?

As others have stated, it’s very system dependent.  But I’d venture a guess that in most systems a preamp is critical to the end result you hear.  Over my many years of listening/learning my two absolute biggest surprises were:

1- the preamp can make a huge difference in a system’s performance, and in my system the pre makes a much bigger difference than even the amp and is only behind speakers and the room in terms of its overall influence and impact on sound (again, very system dependent).
2- subwoofers can absolutely transform a system in terms of dramatically improving imaging and expanding the soundstage (it ain’t all about that bass).

These were the two biggest smack me upside the head/I didn’t see that coming moments during my long audio journey, FWIW in the context of your question.  I’d HIGHLY recommend at least demoing a good pre in your system to see what you hear for yourself — I bet you’ll be pretty surprised.  I sure as hell know I was.  Have fun with the journey. 

As others have said, it is very dependent on the rest of your system. But unless you have a single high-level source with an excellent built in volume control (such as @mikelavigne 's MSB DAC), a good preamp can make a significant different to the overall sound quality.

In my experience (45+ years in this hobby), the speakers and room are still the most important, but the preamp is probably next in it's effect on the sound. If you're including a phono stage in the preamp, it's even more important. 

WOW mikelavigne ! You’re in rarified air, or rather the stratosphere. Good on ya. I love the listening room you built.

https://darko.audio/2015/11/the-select-dac-ii-msb-technologys-90000-da-converter/

I used to run a well-regarded passive line state (whose name escapes me) with my McCormack DNA-1, with CD source only, and loved it. McC made their own passive line stage that is still coveted when upgraded by Steve McCormack.

My sources are all digital, and I have thought of either getting one of the Tortuga passive stages (straight wire, no gain) into a DAC and then my amp, or something like the Chord Hugo TT2 DAC using that as the preamp too. And then I think that maybe a tube preamp would be fun, as I’ve never had tubes. But my whole system costs less than an exotic set of speaker cables!

Good thread, but the frustrating part is not being able to mix and match the various options in auditioning pieces (within budget), and trying to dial in the synergy. I have a short list of amps and preamps I like, but I have no idea which ones would play well together if of different brands. Therefore, I wonder if going to an integrated (Pass 60, Levinson, Aesthetix Mimas, Simaudio 600i V2) would alleviate that frustration, and then the DAC becomes the main variable. Hmmm.

The preamp is as important as any other component in the system. If any one component is more important than the rest it would be the listener.

WOW mikelavigne ! You’re in rarified air, or rather the stratosphere.

Actually no, just a few miles outside North Bend, way below Snoqualmie Pass, not even 1200 ft, well within the troposphere.