you should buy a nice preamp with a phono stage, or look for a headphone amp with one.
the pre-amp would give you something to work with for future upgrades when time and funds allow.
one other option is an active speaker system there are a couple out there that have phono stages. Audioengine comes to mind around $300.
hell something like a Shitt Audio; Mani phono $129- Fraya Pre-amp $699 and a set of active speakers for the rest of your budget would give you a pretty good starter system hell I bet it would quite be nice. you’d get head phone and speaker playback.
oh just thought of another idea. ifi audio retro 50 system right at your budget.
https://ifi-audio.com/products/retro-stereo-50/