Within your budget ...
If you're keeping those speakers, you should check for dry rot on the surrounds of the drivers. Fixing those could be the best money you spend. I would also look at how you have your speakers installed: location/posittion, on stands, how they are coupled to the stands or floor - these improvements can make a big difference without costing much aside from your time and patience to dial them in.
After that, new cartridge for turntable (and good installation!) and outboard phono stage. Good options for both from Rega, Denon, and others.
After that, cleaning all your connections and replacing cheap patch cables and lamp cord wire with decent wire from Belden, Blue Jeans or others. Easy to spend a fortune on wire, but I do find basic sold brands can make a really nice improvement over old "free" stuff that came with the gear.
A streamer could open up your system to the world of digital, and so could a blutetooth receiver or cheap cable that connects your phone to an open input.