Phono Stage, Cartridge, DeGritter...which one first?

I’ve been cleaning my records in the sink now since 2007. That’s when I quit using an US. Lots of really bad, piss poor advice! ^^^

Unless you have more $$/€€/££/¥¥ than brains. Many in here do.

Keep your P6. Upgrade your cartridge. That’ll get you the most from what you have. Then to match your cartridge (later), upgrade your phono preamp. Again, that’ll maximize your setup; you’ll be at the limits of your table. Then, upgrade your table.

See how this REALLY works?

Sorry to burst many bubbles, but you’ll hear an improvement upgrading your cart first, then preamp, then lastly your table. You have to push to find the limits of what you have; you start with your cartridge. The other components will then rise to the level you set with your cartridge.

Expertly cleaning records (pristinely clean!) needn’t require more than $20 of materials. In the last 10 years I’ve set up 8 record reseller businesses on how to expertly and cheaply/quickly clean records. They’re all still in business and doing well. If you’re spending more than 5 minutes per record to clean and dry them, to absolute cleanliness, you’re doing it wrong.

I have a clearaudio performance DC with tracer tonearm along with the Hana ML1200. I had a musical surroundings Nova III and upgraded to a Rogers. How many hours do you have on the cartridge? I'd say get your hours out of it and then take the 500 trade in towards an upgrade that musical surroundings gives you. In the meantime upgrade your table or phono stage. Buy a 500 cleaner like a project. 

A cheap ultra sonic solution as suggested by @neonnight coupled with a Project VC-S2 ALU to vaccum the record dry from a distilled water rinse. The Project is $699.

I like to use Tergikleen. 10-20 drops per gallon of distilled water. Then a distilled rinse.

Tergikleen is what the Smithsonian uses to clean and preserve its vinyl records, from what I’ve read.

You’re all in for around $1200.
Listen to some nice clean records to help you decide if a cartridge or a phonostage is your next right move.

The Library oh Congress, the BBC, many dealers and others use the Keith Monks RCM. Dealers use them as a service for clients and some charge. It is a vacuum system that uses a German medical grade vacuum pump attached to a tone arm like arm with a nozzle at the end. Their fluid is also special. Their model without the fluid pump allows one to just apply the fluid with a squeeze bottle. It cost much less. You apply the fluid and then spin the record while holding a brush down. The the arm placed on the label moves like a tone arm in reverse over the record vacuuming up every bit of fluid and dirt. It does this unlike other vacuum VPI types and ultra sonics.
Upgrading to the P8 is a good idea. It is very much like the P10 for a lot less. And improve you phono stage, then think about a RCM.

Clean records are a must.  I have been using a Nitty Gritty for many years and it did a fine job of cleaning the record, visually.  I have focused on my turntable, phono cartridge, and phono stage first and have made significant sonic improvements every step of the way.  Then, I upgraded my record cleaning system to a Degritter.  I still use the Nitty Gritty for used records and once cleaned by that vacuum RCM the record goes to the Degritter.  The results with all of my records (current collection or used purchases) after US cleaning in the Degritter is that I am a little closer to the music.  For example, the music is more detailed in a manner that I am hearing a sizzle cymbal trailing off for a longer period than I had heard it in the past (same record, very familiar with it).  Vocals (again, same records that I am familiar with), if recorded well, I will often hear lips smacking or vocal chords vibrating that I had never before heard.  Many other examples, but that should give you a good idea.  These finer details in the recording, however, will not be revealed by US cleaning if the turntable, cartridge, and phono stage are not up to the task in the first place.
So, as I did, I can recommend that you first focus on upgrading the analog front-end, and then upgrade to a US cleaner.  Until then, be sure to keep your records clean.  The Record Doctor is a very good entry level vacuum record cleaner, low cost, it does a great job, and it's made by Nitty Gritty for them (a quality product).  I can wholeheartedly say that the Degritter is an excellent choice, providing it is within your budget.  It is engineered from the ground up to clean vinyl records.  It is not an off-the-shelf US tank made for cleaning jewelry or other items.  It does the job better for vinyl than any of its peers, but it's also a lot more expensive.  
I hope this helps you make a decision(s).