Upgrading my beginner setup and not sure how to allocate funds. New cart, table or amp?

Your first step should be replacing that ten year old cartridge. BTW, Shure does not make cartridges anymore!

I don't disagree, but I also don't want to sink a bunch of money into a new cartridge if I'm upgrading the turntable anyway. 

Go for the Rega P2 and put an Ortofon 2M Black in it. That will make you a really happy camper. 

No. Get the Technics 1200GR and a Nagaoka MP110. Always get the best source you can afford. Save for a few more weeks, max the card! Then you won’t have to worry about the front end when you go to replace the amp. If you get a lower-end table, you’ll be playing catch-up when you upgrade the amp.

Personally, with your setup - I would recommend one of two approaches
…
#1. an external phono stage and replace the cartridge...

Something like the Simaudio Moon phono stage
https://simaudio.com/en/product/110lp-v2-phono-preamplifier?v=3e8d115eb4b3
https://www.soundstageaccess.com/index.php/80-leaked/924-simaudio-moon-110lp-v2-phono-stage

This phono stage provides excellent performance and will improve the sound - plus, allow you to expand into Moving Coil at some point (if desired)

Any of the AT cartridges would probably be a good match for your turntable.

#2 - If replacing your turntable you are really looking to do - take a look at Music Hall MMF 3.3, or 5.3 or better still the 7.3. They all come with Ortofon carts


https://www.needledoctor.com/hifi-equipment/Turntables/BD-Turntables/brand/Music-Hall

The 7.3 is a great TT and has lots of advanced features
- a dual plinth for better vibration isolation,
- Carbon Arm,
- isolated DC motor for quieter operation and great speed control,
- belt drive to the outside of the platter for better speed control
- high mass acrylic platter for great dynamics and details

https://www.needledoctor.com/Music-Hall-MMF-7-3-Turntable

BUT WAIT - is there a third option?...

#3 - I believe the Best Bang for YOUR budget would be the Music hall 3.3 ($700 for the Black OR $800 for the Walnut version), together with the Simaudio Moon 110LP phono stage (around $400) - which would come in under budget and sound great. 

You’d even have enough left over for some really good cables OR upgrade the phono stage power supply to a linear power supply - my preference:-)

For years I tried an in-amp phono stage in a really good class A/B amp, then moved to a couple of different "budget phono stages" , but it wasn’t until I stepped up to a more expensive and more configurable external phono stage, that I realized what I had been missing all along.

I now have the Simaudio MOON LP5.3 RS.https://www.stereophile.com/phonopreamps/307sim/index.html
The nice thing with Simaudio Moon gear is - as they develop their higher end products, features and circuits in those products flow down to their entry level gear, making it exceptional value whilst providing excellent performance.

Phono stages inside amps are generally "make do" products designed to a price-point in order to sell the amp on its features. They work, but seldom deliver the resolution, dynamics, clarity and imaging of good external phono stages.

Simmaudio Moon are experts in the phono stage business and all their products provide great reliability and sound quality AND you get a 10 year Warranty.

Hope that helps - Steve