New speakers for turntable ($500 range)


I’m looking for new speakers to go with my turntable, and hoping to stay below $600.  I also just picked up a Keiid amp. Any speakers you’d recommend?  What should I consider for speakers in this price range? How important is speaker cable?  Currently running 16 gauge copper rockfish.
time2listen
I think mesch has given you some very solid advice. With his suggestions, you get out from under your current amp,and stay within your budget. My brother owns the yammy A-S301 and has it paired with Wharfedale Reva -1’s. It sounds very nice,for not a lot of cash. 
These go on sale every few weeks for $300. Grab them when they do. They are amazing. Check out the reviews on YouTube too. https://www.jbl.com/loudspeakers/STUDIO+530.html
Thanks all for the great advice and recommendations.  Time for me to digest it all and make a decision.  I’ll post what I end up getting.