Allen...to get to your original question of how to allocate the budget when thinking about analog set-up, the way I think about it is that each of the component parts plays an important function in delivering the overall SQ. Here's how I think about it:
1) Turntable: function of the turntable is to provide 3 things: a) speed stability, b) as little wow and flutter which is a function of the bearing and platter design/assembly, and c) a means to reject or dissipate energy before it reached the tonearm/cartridge and this is a function of designer's choice of how to do that (suspension vs. high-mass designs). So generally speaking the turntable's job is to provide a speed-accurate, stable platform to rotate the black wax.
2) Tonearm: its function is to provide a stable platform for the cartridge in a manner that will best optimize the cartridge to track the grooves in the LP and again to reduce/reject any energy from reaching the cartridge.
3) Cartridge: its job as the transducer is to perfectly track the LP grooves and to convert that mechanical energy into electrical signal that shoots to the phono (reverse of a speaker) and obviously in this systems approach of a turntable set-up in a way this is your source. This also has the biggest impact on the kind of sound and provides you with the most flexibility to tailor the sound to your preferences.
4) Phono preamp: obviously its job is to take the very low-level electrical signal that its fed from the cartridge, apply RIAA equalization curve (in most cases) and amplify it to a line-level signal that can then feed your line level preamp.
So why do I go through this quite obvious description. Well because it's obvious here that that all these are important functions and are inter-related and short-changing one component, then sub-optimizes the system as a whole (weakest link in the chain argument). So in a $20K budget, I would put $4K into each component (turntable, tonearm, cart, and phono), and put $1-2K into phono cable, another $1K towards record cleaning and set-up tools, and then the rest ($1-2K) to buy LPs - new and used - since you are starting from scratch.
Finally, the way I think of it is you want the turntable and tonearm to be as neutral as possible because they provide the fundamental platforms of speed stability, accurate tracking, and vibration rejection, and where you want to tailor the sound is with your choice of cartridge, and some people also do some SQ shaping tuning also with phono pre (again tube vs. SS, accurate vs. romantic, etc...).
You have received many good suggestions on various set-ups but I thought it might be helpful to think about the systems way of building a tt set-up and how important each part of the chain is in guiding you when thinking about where to spend the money. Nothing earth shattering here I know but hopefully it's helpful to you.
In the used tt space, I would add Basis Audio to your thinking and would echo the recommendation for Graham tonearms. In the cart space, I know you have received lots of recos for Ortofon and Benz, which are excellent, but here is where youvcan think about the rest of your system and shape the overall sound you want and there are many excellent options (from Lyra on one end of the spectrum to Koetsu on the other end and everything in between).
looking forward to see where you end up
I will probably allocate a fraction of that amount to get started, maybe half, but with some wiggle room to go over. 
Just bought a small stash at Princeton Record Exchange tonight and picked up this interesting little gem:
