Analog upgrade path

Cartridges wear out.

Turntables don't. Neither do tonearms. Nor phono stages. Anyway, investing in any of them will get you further than a cartridge, even a Koetsu (which I own). IMO.

I had a Technics SL1500 in my room for a time, paired to an air bearing tonearm and a good cartridge. Didn't care for the sound compared to my belt drive tables.

Since you are considering staying with the SL1500, you are obviously content with a non-suspended table. In that case, an air bearing arm may work best for you, and yes, one of them is affordable.

I use two air bearing tonearms from Trans-Fi, the Terminator (don't blame me, I didn't name it). At about $1200, the best buy in high end audio, but won't work on a suspended table. That's where I'd go: (1) Terminator, (2) belt drive unsuspended table (3) phono stage. Save what you didn't spend on cabling to get a decent cartridge, and when you've got lots more to spend, upgrade the cartridge.

That way you spend money on non-depreciating assets instead of putting money into a depreciating asset and getting less bang for the buck (a cartridge). IMO.

I know almost nothing about cartridges but I do know that Goldring 1042 sounds quite good with Nottingham Spacedeck/Spacearm and Acoustech PH-1 phono stage. I am sure there are better MM cartridges, both vintage and modern, but for the price new it would be hard to beat, maybe some AT on sale. I got mine from the UK, analogueseduction.net
Cheap budget phono is never a good idea. In your case, I would upgrade phono stage and maybe cartridge first. But if you wanted to upgrade everything step by step then yes, I would probably start with the turntable. Depends on how much to spend and when. Or maybe wait longer and then upgrade everything at once. That's what I did.

The link will show you a few recent responses from MK1 users.
Reply 11 is worthy of consideration.

https://www.lencoheaven.net/forum/index.php?topic=31031.0

I personally own Vintage TT's and like to think that a overhaul with a modern thought for available materials works in favour of the Performance to become on offer.

When choosing a TT to be used as the Main TT on the System,
I would have electrics circuits assessed by a competent person and the Circuits Boards / Components thoroughly cleaned.

The Platter Spindle Bearing would be next on the List to be Investigated.
Using gentle finger applied pressure to the Spindle Checking for any sensation of a Spindle showing it is allowing a Side Ways Movement.
If a  Vintage TT is with a unknown History, or known and a exchange of a Bearing Housing Bush is not believed to be needed,
learning how to remove and flush the insitu Bearing Housing Oil will be the next on the List.
Followed by learning the Oils available today that will be the best to be used as a the New Oil. ( There are Oils Today designed to work at their optimum in a setting that is very similar to a TT's Spindle Bearing Housing, especially with modern additives that allow for a decreased friction and Drag on lubricated parts.)

Looking at the underside of the Chassis in the Link above, it looks like it the Chassis can have a Underside Treatment Applied of a application of Modellers Clay such as Newplast ( Reversible) or,
a Bituthene Tape ( Residuals would be left if Reversed).
( This as a Chassis Treatment is cheap to achieve,
it can be investigated to decide if there seems to be a merit to be achieved in carrying out the Treatment )

Again using the info in the image in the Link above, it seems that there is a opportunity to use a Independent Disc for the Tonearm Mounting Base.
(There are a large selection of materials that could be trialled as a substitute for the Original)

The same is looking like it can be said for a Tonearm Selection as well, if the Tonearm Base is exchangeable.
(As the slight variations of a Tonearms Geometry Set Up needs can be catered for in a Bespoke Produced Tonearm Base ).

In my View when much of the above is achieved ( not too difficult )
a well thought out Investigation into Mounting the TT will be very worthwhile as a undertaking.
Selecting a Rack Shelve Material and Footer or Wall Mount Shelve Material and Footers, will effect a presentation from a TT,
in cases exchanges of either Shelve, Sub Plinth Materials or a different Footer Design can produce a very desirable presentation.
Shelves and Sub Plinth Materials and Footer Types when carefully  selected for a TT really be a beneficial time taken to assess and select.

When all the above is in place, i.e TT > Tonearm > Cartridge >
TT Mounting.
The how to get the best from the Set Up,
by trying New Types of Electronic Devices in the System will be quite revelatory in what can be learned of a devices contribution.

Have a few different Platter Mat Materials to use as well,
( Loan some if possible )
I have auditioned Devices in the past that were underwhelming, and not comparing in a desirable perception to other used devices.
When a Platter Mat was exchanged the performance was vastly improved, and much wanted. 
I have Leather, Felt, Foam, Rubber, Ceramic and Gunmetal.
The effects can range from Bloomed > Richness > Perceived Weight >
Lean. 
I have used a few of the above practices beyond my system,
by taking My chosen Sub Plinth > Footers and Platter Mats to other Homes and used them on other owned TT's.
The response from a TT owner is sometimes Jaw Dropping as the results of the exchanges are so noticeable. 
I don't encourage a presentation type, this a individuals unique choice,
I enjoy helping the person get closer to their wish list.

Well there are a few Two Cents Worth snippets of how I use some of my 'Spare Time' around preparing my owned Vintage TT's for a life at the front of the System.       

I would dump the turntable. Buy a pro-ject classic evo and a hana el cartridge (crazy good for $475) or both the goldring eroica lx and Denon 103. Alternatively, buy a Music Hall mmf-7.3 with pre-installed ortofon 2m bronze. Then grab a pro-ject tube box ds2, a killer tube stage for a grand...go look at the reviews. It slays stuff costing much more and has all the adjustments you would ever need. Lastly, buy an apollo turntable shelf, built like a tank in the UK. If you want to throw money away on a 5k phono stage, go right ahead....there are plenty of phono stages available for a grand that are fantastic. Another would be the Tavish classic @ $699. Even the tavish adagio is only $2500.
I speak from actual experience, as I own all the above, with exception of the adagio. You will need to spend 10k or far more to get significantly better analog sound. One last thing I forgot to mention, I would highly recommend the Jensen Mc 2rr step up transformer for the both the Hana el and Denon 103 cartridges. It is an amazing SUT for $599. The Jensen has a built in load of 430 ohms, perfect for both cartridges. Also, use dedicated low capacitance short run phono cables such as those made by Atlas cables or Rothwell. I use .5 meter lengths.

You don't say what cartridge you are using.
It isn't a good idea to upgrade turntable and skimp on the phono amp.
Getting a nice phono stage will certainly be the single best sound quality for money move for you now..

I have had many ARC pieces; until last year I had run an LS5 with a PH2 - both fully balanced.  This lasted me for trouble-free years 25 years and I liked the ARC flavoured sound.

I have upgraded to a Ref 6.  After a two month loan, I went with the van den Hul Grail SB.  It may be outside your budget but IMO it is a good bit better than the top-end ARC and a lot better than Boulder 508.  Overall this upgrade has transformed SQ by a quantum leap.