Which to upgrade first: Turntable or Phono Preamp

There is Nothing wrong with that turntable, it is beautiful and a pleasure to use. however, personally I would have opted for the classic sb with speed box built in. I own the sb classic and hana EL and it is a terrific turntable/cartridge combo. I would look to replace the phono preamp. Get a tavish design the classic or the vintage tubed preamp ($699/$729). The difference is the tubes used with each. I would then also advise you to use a Jensen mc 2rr, a 1:10 sut ($600). The Jensen has a fixed load setting of 430 ohms, perfect for the Hana. Connect the sut output to the MM section of either aforementioned tavish (47 k ohm) and enjoy! Oh, if you get either tavish, change out the tubes for some vintage nos tubes! I’ve got a RCA 7025, GE 12au7, and a Sylvania 5751 installed in my classic and it is great!

One last thing to add to that pro-ject would be the Stein music mat, it is great but expensive @ $249. Available from Galen Carol. For a cheaper mat, I’ve had success with the hide in the sound leather mats, very thin and of high quality.

Both the Jensen sut and the Tavish design preamps are made in the USA. Both companies also pick up the phone and are great to deal with.
The tone arm on the your classic is of a great design. It was chosen by Linn for its $4300 MAJIK. It is also versatile at 13.5 grams effective mass, allowing you a greater choice in cartridges.

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)