Where do I start-amp or speakers ?

Amplifier speaker integration is only hard if your speakers have a hard to drive impedance curve, and if your amplifier has a high output impedance.

Of course this statement is not 100% true, which is why equipment matching is important.

An example of an exception is the Quad or Sound Lab ESL, which does not sound right if the output impedance of the amp is low. There are other examples of course (the Acoustic Research AR-1, the world's first acoustic suspension loudspeaker, is probably the best-known example as it is so famous; it was designed for an amp with a 7 ohm output impedance).

Start with the source components and invest most of your budget there. A great turntable and preamps can make inexpensive speakers sound great. A power amp can only amplify the quality its fed into the speakers.  Given your budget, I would spend 10K on a  turntable, 4k on a phono preamp, 4k on a preamp, 4k on a power amp and 2K on speakers. You can upgrade the speakers later. 

Opinions vary greatly as usual, but it has always been my (limited) experience that the speakers make the largest difference in sound. Everything is important from the source to the preamp to the amp to the speakers, but when I change source or preamp or amp the difference is always noticeable but it is incremental compared to changing the speakers. Changing these other components may give you higher resolution, more defined bass, and any other number of attributes, but changing the speakers has always been more significant. They are the most variable in terms of distortion, bandwidth/frequency response, etc. Again just an opinion but speakers first.

Absolutely, it is all about the simple mathematics of relative error. There is litle point in worrying about 0.001% difference in distortion in the electronics if the speakers have 1% or more. The same is true or frequency response where electronics are usually perfect wthin 0.2 dB, but speakers may easily deviate from flat in even the mid frequencies by a few dB. It is simple high school maths. And for those who don't like science: you can hear it.

well, I already voted once: speakers first.

But then I reconsidered this thread and the OP original question.
Most ppl are responding, e.g, "I WOULD do this first .... " versus "I DID this first ...." . 

IOWs: theory vs reality. I'm not in the market for amps or speakers. I have 4 pair of speakers and 4 amps, 2 preamps that I am comparing to each other with different electronics: trying all permutations to compare. I enjoy this process, it is "fun" to me, tho may not be to others. 

My point is that if I were in the position of choosing speaker vs amp first, I wouldn't do either per se. I would do what I have already done: collect a few amps and speakers to compare rather than put all my eggs in one basket and buy "speakers first, then amp" or "amp first, then speakers". This method works for me. 

thinking back, I came to my present position by compiling my top 5-10 speakers I am interested in, irrespective of amp. Then make a list of 5-10 amps, irrespective of speakers. Then cross-match electronics, tube-vs SS vs class D, impedance, etc with the electronic/power requirements of the speaker. that will give a short list of amp-speaker pairings that would theoretically work together.

Then review the 'short list" for realistic considerations: the pairings may look good on paper, may seem good, but may not fly in reality. Like me, you might think to yourself, " I really think these speakers are the ones, but I'm not sure if amp A/B/C will produce the best sound ... also depending on the Preamp.

I'm just sharing how I have, over the last10 years, learned to mix and match gear, and avoid the pitfalls of "there is only one combo out there for me and my room". there are oodles of combos that will sound good in your room, but only A vs B vs C, etc comparisons will reveal the best sound your ear.