You dont need a pre amp and amplifier.
Some Turntables come with a builtin pre amp - dont need 2 amps!
If Turntable has no pre amp then yes you will need to go through an amplifier.
Try running the turntable from the same electrical outlet as the computer ( to give common earth)
Do not run power cables parallel or near the RCA cables.
Move the Turntable away from computer, short cables are not always the answer, I run 2m cables with no problem.
Ensure other electrical units are not close by or at least turn the off. Printers / scanners etc should be off.