The small basic inexpensive Onkyo home theater in a box speakers are the sound quailty bottleneck.

If you are looking for better sound quailty then upgrade the basic inexpensive plastic Onkyo home theater in a box speakers first since the speakers are the sound quailty bottleneck, not the turntable.

5x speakers for under $200:

• https://www.amazon.com/Jamo-Studio-803-HCS-BLK-Cinema/dp/B07JJ5VKHL
• https://www.amazon.com/Jamo-Studio-803-HCS-WH-Cinema/dp/B07JJP96NT

Or start with a better pair of speakers and add a matching center speaker later, keep using the Onkyo speakers for side surrounds or upgrade those later too and they don't need to match the front speakers:

• 5.25" Neumi BS5 $109 plus center.
• 5.25" Polk ES15 $299 $219 plus center.
• 6.5" Klipsch RP-160 $549 $195.

Then later upgrade the subwoofer:

• 12" Dayton SUB 1200 $179 for example.

Audio Guides, Speaker Placement, Accessories and Vinyl Care

Whatever you do go with discrete audio components. You could go with a Home Theater in a Box set like this Yamaha YHT-5950U. Or start with a 3.1 setup and add rear speakers later as budget allows.

• Check your local Costco for the Denon AVR-S760H (has been on sale in store lately as low as $250) or the Yamaha RX-V385 would be a (significant) step down option. Even at Costco's regular in-store price of $350 the Denon is likely worth the extra if you can swing it thanks to its HDMI 2.1 support and 7.2 channel amplification.
• A center channel like the NEUMI CS5.
• Front surrounds like the NEUMI BS5.
• Monoprice subwoofer for some kick.

Later add rear speakers as budget allows. A second set of NEUMI BS5 or a set of Micca MB42X would round out the setup nicely. If you get the Denon S760H you could also add a small set of front Atmos height speakers like the Micca COVO-S for a 5.1.2 setup.