If you started from scratch - what would you do?

I'd replace the integrated. If you get something with a built in dac I'd try ripping cd s to computer and playing from there versus current CD player and go from there.

I prefer to keep my components separate. With patience, I found I could get the best of each type of component. Also, replacing and/or upgrading is much easier.
Amplifiers are a relatively stable platform. Purchase a good one and it can provide trouble free enjoyment for a decade.
DAC's develop much faster (than amplifiers). IMHO - unless you're buying a statement DAC or one that can be upgraded, keeping a DAC for a decade seems unlikely - especially with less expensive DAC's.
New better performing cost effective DAC's continue to be brought to market that keep getting better. And remember, especially with DAC's, yesterday's price performing class leader is usually discounted once a newer (and usually) better model is brought to market.

Something like the Playback Designs IPS-3 might be worth considering. You get an integrated amp and state of the art DAC all in one component. You could use your CD player as a transport and the IPS-3 DAC to spin your current CD's. And you can start the transition to DSD downloads since the DAC is fully compatible.

If I had it to do all over again, from scratch - I would devote to vinyl - why, because I had to spend over 10K in DAC to compare - money better spent in music