For that authentic roadie feel, I’d go with 25c tyres. You may have wider rims for Cx, so these will fit better. Everyone has their favourite brand. Mine is Schwalbe for robust tyres that roll well and grip. I’m running 25c Durano Plus and they are excellent – available folding. I also have 25c Marathon Plus, again very robust and good grip. Others are Durano S, and Ultremo (23c), but Ultremos are not for winter use. I’ve just ordered some Ones in 25c with latex tube.
I’ve tried Continental and didn’t find them grippy in the wet and cold. They were cheap, however.
My recommendation would be Kevlar folding Durano Plus or Durano S, either in 25c run at 90/100 PSI front and rear. Don’t skimp on inner tubes, either. I run Supersonics as a luxury, but aim for a decent brand and 100g.