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. Avoid those two problems and there is no real issue unless you are a hypochondriac.
If the budget is indeed 8K for a medium sized room, I would allocate most to the speakers: Harbeth SHL5+ are perfect for such a room, and they are easy to drive. Harbeth make some of the cleanest, musical and non fatiguing speakers on the market. They like a bit of power, so why not go for an affordable solid state pro audio amplifier like the 2x350 watt Yamaha P3500s? See here for a test that proves that it is perfectly suitable for domestic use: http://www.homecinema-fr.com/forum/amplificateurs-de-puissance-haute-fidelite/mesures-ampli-yamaha-p...
I recently bought the slightly weaker 2x250 watt P2500s for my son, and the sound quality is just perfect. The variable speed fan never comes on in domestic use. And as a pro audio unit it has balanced inputs for lower noise. Built like a tank.

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.