And the working budget is ...???
After looking more deeply, it appears to be UNDER $600 for Amp/Speakers and about $400 for the Turntable. So, less than $1000 system total.
That is a pretty considerable system.
One suggestion would be the Edifier R2000DB which are 5.25" speakers with TWO Aux inputs, Optical, Bluetooth, Remote Control - $250/pair.
If you want compact, that is compact. But it has a limited number of inputs. Though one Aux for Computer, and one Aux for the Turntable would get the job done, as I understand it.
You can find many video reviews of the R2000DB
speakers on YouTube.
All you would then need is a Turntable. You can spend $400, but it is probably not necessary.
Not necessarily the greatest turntable, but the Denon DP-300F
is an Auto-Turntable and can be bought with a cartridge upgrade for roughly your budget. The nice thing about this turntable is that it is NOT a manual. Simply push one button and the motor starts, the tonearm lifts and moves to the record, at the end, the tonearm lifts and move to the rest, and shuts the motor off. Very easy and fail safe to use.
Denon DP-300F Auto-Start/Auto-Stop Turntable -
Denon DP-300F Auto-Start/Auto-Stop Turntable with Ortofon 2M Red Cartridge - $419 -
The Denon DP-300
has a Phono Pre-Amp built in (switchable) so it doesn't need any external component.
That's a complete system in three pieces total for about $670.
There are better Edifier speakers, but they typically only have ONE Aux in. The Edifier S-series are near Studio Quality speakers, and the price reflects that -
Edifier S2000 Pro - 5.5", 1xAux, 1xOptical, 1xCoaxial, Bluetooth - $399/pair -
The S2000 Pro plus the Denon DP300 would be about $820/ set.
Edifier S3000 Pro - 6.5", 1xUSB, 1xOptical, 1xCoaxial, 1xAux, Bluetooth - $799/pr -
The USB would allow a direct connect to a computer, the Aux to the Turntable. All the Edifier Speakers are available from Amazon.
Personally, I would start without a Sub and see where it goes. Many people are more than happy to just listen to bookshelf speakers, especially if space is limited.
The Edifier do not lend themselves well to adding a Subwoofer as there is no Sub-Out.
Nothing wrong with the very fine list of equipment you originally suggested, I'm simply offering a very compact easy to use, easy to move system for under budget.
Also the advantage of the Edifier is that they have a Remote Volume and Source select control. When you are at a desk sitting at a computer, a Remote control is not really necessary. But if you are sitting back in a lounge chair, it saves getting up to control the volume, and you can probably get the TV, BlueRay, and Edifier to all work with a Logitech Universal Remote.
Again, you suggested very fine systems, I suggest the most minimal component system that will be easy to use, very compact, and modestly priced.