I was always trying to dampen and smooth out the harsh sound of digital.
I know any number of audiophiles, some with systems costing well north of $100K, who've spent years and dollars trying to do just that. They typically end up with a bunch of rosy, smooth and soft sounding components that smother the life out of the music - all to make digitized waveforms tolerable.
When they (re)discover analog, they have a hard time shaking the (false) concept that their components need to protect them from the sound by gentling it. Natural waveforms don't need gentling, they need the most honest and accurate reproduction your budget and skills can achieve. Whatever level you're at, or hope to be at, the first thing to do when shifting to analog is to appreciate that honesty in a component is a good thing, never a bad thing. This is true of every component in the system.
And yes, record cleaning is essential. Playing any record, old or new, before proper cleaning guarantees inferior sound and risks permanent damage. Headsnappin' explained why. Welcome to vinyl madness. Enjoy!