Logical upgrades to a DD turntable.

If you know how to solder and have even an elementary understanding of electronics , there are a few things you can do like improving the wiring and improving the quality of the RCA jacks, etc. But if you are willing to spend some bigger money, the giant leap would be to buy a new turntable in the 1200 G series. Although they look like your turntable, the 1200 G series turntables are in every way superior.

In fairness, I forgot to mention also that the company KAB sell a number of add-ons that also improve the 1200 series turntables. But none of these devices, although effective, can turn a 1200 into a 1200 G series. If your budget doesNot permit buying an entirely new turntable, you ought to check out the KAB website.

You have to change a cartridge first of all, m44-7 is extremely high output MM with Bonded Conical tip! The key of this DJ cart is high output and durability, but not sound quality. 
Get yourself a proper Hi-Fi cartridge with advanced stylus (nude diamond, not bonded). If you want brand new then look for Audio-Technica with MicroLine stylus. 
You have to start from the cartridge, it will be the most noticeable upgrade, after that you will have to rewire your tonearm with Cardas or Discovery (flexible internal wires) and external shielded phono RCA cable. 

+1 from chakster and also the Audio-Technica with MicroLine stylus. The stock arm & Headshell would prefer a lighter tracking version while heavier headshells would open you up to the 2gm+ VTF versions (6 one way & half a dozen the other). On 2nd thought, the stock tonearm would gain a more useful VTA range if the new cartridge incorporates around a 3mm spacer on top under the headshell. From what I recall, the stock arm really doesn't go low enough for neutral VTA and any mat over 5mm thickness makes the record spindle disappear. Better headshell wires such as the Audio Technica AT6101 from LP Gear and replacing the stock RCA cables with some twin leads made from Mogami W2549 might be easy to attempt. KAB has many good mods such as tonearm rewire kits if you want to keep the stock arm, Strobe defeat to reduce motor noise, sorbothane type footer boots for even more mechanical isolation as well as an outstanding outboard power supply (prefer the switched mode PSU version) that bypasses the internal transformer while providing an upgraded regulator at the motor. These 'tables can really work if you put in a little effort. Bearing, platter and mat upgrades are also possible, with much gain to be had with minimal reworking of stock parts.

What is the most obvious tweak / upgrade for this type of turntable before spending substantial money on a better cartridge?

Sorry, the others must have been so eager to post they missed this one entirely.

There’s a couple really cheap yet effective tweaks / upgrades that will improve this table a lot. I have a very old SL1700, hasn’t been used in years but I tried all this and know it works.

Dirt cheap yet super-effective: put the table on a sand box. Doesn’t have to be huge. More is better but an inch or two of good packed sand is fine. Mix it with a little mineral oil so it packs down and stays put with no dust. Used since like forever because it works- and is cheap and easy to do.

For only a little more money but even bigger improvement: springs. Every size is there on eBay but it takes a lot of searching to figure it out while Nobsound springs are adjustable to a wide load range and only $30 which is why I recommend them. Yes Townshend are a lot better, but they cost more than your current rig. True, they will elevate the performance of your current rig to where you can’t believe. But still: money.

Next after these two is fO.q tape, thick or thin your choice, either way about $60 for enough to make a serious improvement in your system. Tone arm, platter, plinth- try small pieces, see how it sounds, slowly gradually add. Also works great on speaker baskets, and inside components on circuit boards, etc.

From here on, either you get into more expensive tweaks like Synergistic PHT and ECT. Now you are looking at around the $200 range where you could get decent phono leads. If you do go phono leads do NOT get anything that goes to RCA and makes you have to buy an interconnect. DO get phono leads that run continuous from cartridge to phono stage.

Something to keep in mind. All the other stuff, sand box, springs, PHT, maybe even the tape, if you ever do decide to sell and upgrade tables these tweaks can all be kept and used, again and again, forever. Phono leads, not so much. No one gonna buy a table without them, nor give you what you paid for them in resale, nor are you going to want to use them in your next table. Phono leads will almost certainly improve the sound. They will also absolutely certainly be a total write-off one day.

Might still be worth it. But go into it eyes open.

It’s all in the details!! Nice catch and yes, eager . . .

I have a Technics SL1200 MK2 that came with the KAB RCA mod.  Not having heard it before the mod, I can't say it's better or worse, but it does provide the flexibility of using better interconnects.

The most impactful and relatively affordable (at the time, they've since increased in price) upgrade was replacing the old worn out feet with some from MNPCTECH.  There are others available.

I have also added the KAB fluid damper and put some fo.Q tape on the tonearm.  Neither had much effect to my ears, but it tracks well, has good bass, and doesn't "ring".  I use very little fluid in the damper, just enough to get the bottom of the paddle in it.  

There are a lot of other little tweaks you can do, external power supplies, disabling the strobe light, tonearm re-wires, and more.

People mistakenly write them off as "DJ turntables".  They are very solid and tend not to have issues with woofer pumping from vibrations when played very loud, which is one of the reasons many DJs adopted them, along with their steady speed and pitch control, and being built like tanks.  

The KAB website is a good resource and there's a lot of good information on Vinyl Engine.

DIY tonearm fluid damper. Free, just takes a little time to implement.

http://www.enjoythemusic.com/magazine/bas/0809/

KAB is nothing special, fluid damper is ONLY for very high compliance cartridge. His cables are not the best and you can get better from Cardas or Discovery for very low cost.

But I will say it again: nothing will give you such a huge improvement as a cartridge, your Shure M44-7 is a DJ cartridge with Bonded Conical tip, replace it with Hi-Fi cartridge.

Do not start from the cables, it’s wrong start.

Fluid damper only collect dust, I have replaced them and don’t use them anymore. Got my pair of SL1210 mkII since 1995 and upgraded with Cardas tonearm wires, Zu Audio Mission Phono RCA cable, Isonoe feet ...

One of the best mat for this turntable is SAEC SS-300.

SL1210 mkII are not in the main system, but I taste nearly all my vintage and new MM cartridges on this turntables with headphones first. Some killer cartridges for this tonearm and turntable: SONY XL-50 (Boron Pipe cantilever), Victor X1II series (Titanium or Berylliym cantilever), Pickering XSV/4000 and Stanton 881s mkII (Stereohedron tip) ... just to name a few for reasonable cost NOS. 

@chakster I agree about the KAB cables, they are average at best.  I am using KIMBER KABLE TAK-Cu interconnects on my SL-1200 MK2.  I had an issue with hum when using MM cartridges and the TAC-Cu has eliminated that.  I forgot to mention mats, I use the Funk Achromat on mine.