SEEKING ADVICE: Which component would you upgrade first?

Corelli +1, If you know an audiophile near your place try to listen to his system , to see if you like it. Then if you like it. Hopefully he can mentor you to put a low cost system if you don’t have the budget.

cheap yet HIGHLY effective: Mad Scientist Graphene Contact Enhancer

First clean all contacts (including power cords) with 99% isopropel alcohol then apply the contact enhancer www.madscientist-audio.com/contact-enhancer

hth

If you want more modern electronics, look at Rotel. Modestly priced, good quality, and nice features in their integrated amps. 

@lukasread I’ll suggest a different route to consider, if not now then at some point, given you said you have a background in music engineering and an interest in vinyl. This route would have you listening to your music in other ways, rather than swapping kit-for-kit in hopes of sonic revelations for a few hundred bucks.

There’s a USD $250-300 device (down from $500 nearly a decade ago) that functions as a phono preamp, a DAC, and an ADC (Analogue-to-Digital Converter). RCA cables from your TT to the device, and the device via USB cable to your computer; and you can digitize all your records to enjoy on the go via earbuds, in the car, on your phone, etc.
KORG DS-DAC-10R

The DAC feature of the KORG will also allow you to connect a USB streamer that can be had for ~$100, or easily DIY’ed for slightly less. There are multiple free software options for this that will also play your personal digital/digitized music library, too (though as a music engineer I suspect you may already have these features via computer / additional unlisted kit).

If you want a way to clean your records and haven’t one already, there are cheap, solid solutions from AliExpress and the like:

Record Spindle Spinner (I would strongly recommend a stronger jet of water than pictured in the article!).

As some folks have mentioned, beware making lateral moves in the kit you already have - yours is solid stuff. For your budget, look for new inroads to using your music if you really are a musician, engineer, and listener more than a new-kit-chaser, being my bottom-line.

@benanders 

the spindle spinner site is down. For $175 I found it a very costly deal compared to actual "standalone" mess and sink-free and vacuuming record cleaner