I'd agree with a lot of the comments here. Listen to it casually for several weeks to let the amp settle in and for you to get use to the sound. Then you can begin to decide on what needs improvement.
A good high quality DAC would solve your harsh CD sound. You could use your existing CD player as a transport if it has some kind of digital out (optical, coax, etc.)
Before I knew about DACs (circa last year), I thought that was just how all digital sources sounded - harsh and bright. Early this year, I bought a Chord Qutest DAC, and now the vinyl upgrades have taken a backseat to the digital upgrades.
Don't forgo high quality cables if you're going this route - not to trigger, cable deniers, but for me it was the difference between really good and transformative.
I hadn't plan to spend as much as I did, but after the fact I found it to be money well spent.