Which to upgrade first: Turntable or Phono Preamp

Find a dealer where you can demo the alternatives before you buy. 

My preference would be to improve the turntable first, as you'll get out what you put in at the front end. But check that out for yourself. 

You don't say where you are but in Europe it's possible to pick up a Vertere DG-1 within your budget, and it will knock socks off your current deck. The Clearaudio looks like a good intermediate step.  

+1 for the Herron VTPH-2A. I absolutely love this phono stage. I did A TON of research prior to purchasing and couldn’t be happier. Call Keith Herron. I did. Super nice guy. He even called me back to troubleshoot a used unit I did not purchase from him after inquiring about buying a new one from him. This is a no brainer if you can afford it. Also, I have the Hana SL with the Clearaudio Concept table hooked up to the Herron. It’s magic. GL!

The pro-ject tube box ds2 is no slouch $999, and worth every penny. Infinite choice in adjustments, load impedance on the fly, up to 65 db gain, capacitance adjustments, subsonic filter, can run two turntables, tubed, combo of jfet/tube on the mc section. A duel mono designed for max channel separation. Available with wood sides to match your classic turntable wood choice! Read this review!
https://www.hifinews.com/content/pro-ject-tube-box-ds2-phono-preamplifier

I own a tube box ds2 with eucalyptus wood side panels, it is beautiful. The sound is glorious, tubey magic. So, in my stable are the previously mentioned tavish the classic, the pro-ject tube box ds2, and the musical fidelity lx lps. All are terrific examples of great design in their respective price range...I’m keeping all three.

You are not going to hear much difference by getting rid of your classic turntable, unless you spend somewhere in the 5k and higher range. By getting a clearaudio or what have you...is a lateral move in my opinion. The main difference you would be hearing in a lateral move such as the clearaudio, Rega, technics, etc....is speed differences. For example the Rega is known to run a bit fast, giving the impression of a more dynamic/energetic sound. When you move up the ladder to a 5k or higher TT such as a Linn Sondek, well then you are playing with the big boys, but you will have an empty wallet. I would max out your classic with the phono preamp upgrade. You are already there with the excellent Hana.
The guru Michael Fremer gave high praise to the classic sb...similar to your classic...
https://www.analogplanet.com/content/pro-ject-classic-sb-superpack-turntable-%E2%80%9Cbrains%E2%80%9..

In fact, there is not a Bad review to be read about either the classic or the classic sb. 

Replace the Vincent with a more refined phono stage. One that is even more adjustable for gain, loading, etc with a quieter noise floor and not so rolled off. The Vincent is beautiful and lush, it is not particularly detailed. Your table and cart are great. (Former Vincent owner here who loved it till I heard one in the same price range that had much more detail)

The turntable is the foundation of your analog chain.  The Concept is a nice entry level table.  I had one, but didn't keep it long.  It was way too sensitive to footfalls in my listening space.  While it may be better on more solid footing, that points to a basic weakness of the table, that it isn't well isolated.

Generally speaking, a well engineered turntable with a good tonearm and good isolation with a modest phono stage and cartridge will sound better than a higher end phono stage or cartridge and a modest turntable.

If the turntable and tonearm don't allow the cartridge to perform at its best, the signal that the cartridge sends to the phono stage isn't going to be improved by a better phono stage.

My advice is start with the table, then get a better phono stage.  You have a very nice cartridge.