You have a good, compact amplifier. It's limitations are that it's got room on the back for just a couple of inputs and you have more. The weakest point of your devices is that AT-LP60 turntable. I would try to upgrade that. I know because I owned one and even the slight bump to the one I have now was a HUGE jump in sound quality.
Your current connections are fine, and the DAC in the Onkyo is a pretty good one. Would you notice any difference between that and the one in the 3020? I doubt it...I think they're essentially the same other than the one in the 3020 is probably a Burr-Brown.