With that budget you should be able to find a really good, very attractive rig that you’ll want to keep. I’d be keeping my eyes peeled for a good used SOTA, Well Tempered, Clear Audio, VPI, maybe a better Rega, AR, or Thorens. The top shelf Technics, Pioneer, JVC, and Kenwoods can also be quite nice sounding, though a bit less esoteric.
Its subjective, but IMO, the trick is get a TT with an arm that’s compatible with a cart that you love. Once the basic TT elements are properly addressed, the carts tend to have the most impact on the SQ. After living with a Nagaoka MP150 with an upgraded MP500 stylus for the past several months, I can heartily recommend giving the MP500 a go if its a match for your TT and pre. It has some incredibly open textured mids, huge soundstage and separation, killer resolution and micro dynamics, and extremely natural delicate treble. It’s in the moving iron class, so doesnt’ need an extra step up.
Enjoy your search