Path of signal from turn table to speaker

 I thought that last part would necessitate processing through the amps DAC as the final step before stereo output.

It has nothing to to with turntable and analog signal. 

If you're listening to digital source then you need a DAC.

For analog source you don't need a DAC at all (it's nonsense).

You need DAC only if you want to convert your records to a digital files for use on your computer or media player. 

The amp must be matched to the speakers, there are low power amps and high power amps. There are also low efficient speaker and high efficient speakers. A low power amp designed for high efficient speakers only. 

Everything will affect the sound, even your room size.

Well no Chakster not quite nonsense. Controversial maybe. My system is digitally controlled. I use full spectrum room control, frequency response alterations and digital bass management. This is all done in 48/192.
In order to use my turntables in this system I have a Benchmark ADC on the output of an ARC phono amp which converts to 24/192. 4 channels of DAC revert all to analog right in front of the amplifiers. So with High Res files I am digital all the way to the amps. 
According to Michel Fremer 24/192 is invisible. He converts Vinyl to digital files routinely using the same program I use, Channel D's Pure Vinyl. 

Mijo, was it really necessary to further confuse the OP? It’s fine to know that you have a analog system that incorporates digital processing and/or is controlled by a digital processor. We all understand that, but it most likely will confuse the OP. To the OP, all the advice you have received above is basically correct. There is no need for conversion to digital or from digital to analog in the pathway from a phono cartridge to your speakers. As someone else wrote, you need a phono stage or a phono section to amplify the signal from the phono cartridge and equalize it according to a certain algorithm that is standard. That amplified and equalized signal then is fed to a line stage. The line stage is really there only to allow you to Select from among several input sources, to include your record player, your CD player, your  tape recorder. The line stage does very little else besides switching, but most of them add a little gain as well. Then the line stage drives an amplifier. In many cases a device that we call a pre-amplifier will contain a phono stage and a line stage all in one box. There are many ways to do that.  Amplifiers do not commonly have any digital electronics inside. A classical amplifier is an all analog device. Like Chakster said, you need to choose an amplifier that has sufficient power to drive your speakers to sound pressure levels that are suitable for you in your particular listening room.

There is one more variant that probably ought to be mentioned. There are also products called integrated amplifiers. An integrated amplifier can sometimes contain a phono stage, a line stage, and an amplifier, all in one box. Other integrated amplifiers would contain a linestage and amplifier all in one box, but no phono section. And that latter case you would have to purchase a phono stage separately.

I think I now understand the source of your confusion. I looked up the Cambridge audio CXA 81, which you say is your amplifier. The product is an integrated amplifier of the type I just described. It incorporates a line stage and an amplifier on one chassis. But it also incorporates a digital to analog converter(DAC). That section of the amplifier should be regarded as an accessory to its major purpose. You can feed the DAC section a digital signal direct from for example a CD player or a CD transport and it will convert the digital signal to analog to feed the line stage and amplifier. This has nothing to do with the basic pathway of the amplification system. I am not sure whether your Cambridge Audio device also has a built in phono stage, but if it does not, you need that also to play records.