Which has greatest influence?

Each component contributes a different area of quality to the overall sound. There is some overlap, of course. Amps and preamps both contribute to dynamic range and resolution, frequency extension, clarity, musicality, smoothness, etc., etc. But an amp cannot increase the resolution over the signal it receives from the preamp. Likewise, even the highest resolution preamp, while preserving signal integrity and passing it on to the amp, cannot control the speakers or deliver the current to improve linear behavior at all frequencies. That's the amp's job.

There are great amplifiers and great preamps. If I had only one choice it would be the preamp FWIW.

Actually it's neither,look to your source that's where it all begins.

The amp/speaker interface is the most important interface (or matching) in your system, right up there with matching cartridges and arms on a TT set up. But once you get that down, the weakest link in the chain saying applies.

FWIW, if I were starting out fresh, or all over, the first component I would buy would be the 'best' pre-amp I could afford and build my system around it. That said, if I were buying new speakers for what ever reason, I would always assume I might need to buy a different amp, just as if I were to buy a new cartridge I might have to get a different tone arm or phono stage.

Just my 2 cents.

Switiching to a tube Pre-amp gave me the most satisfying change in my system. This particular component was the first major upgrade in my starter audiophile system after reading lots of replies to a similar question from earlier forums.