I am looking to spend roughly $1500, though could maybe spend more if I stagger my purchases (i.e. buy a new cart now, buy an amp later, etc.).
Staggered upgrades- great idea! That's how I did it.
If you do decide to go with the cartridge first then do yourself a favor go check out Soundsmith, listen to Lederman and his fixed coil design. Both because they are super value in a cartridge, and also because they are super long term value in that they can be retipped for a fraction of what everyone else wants. All other cartridges are pretty much consumable items. Only Soundsmith with his retip/rebuild program is one you can consider as long term a component as the turntable and arm.