One of the requirements for CE marking, depending on the classification of your device, is that you have a certified QMS in place. The MDR requires manufacturers to establish a QMS (see Article 10 MDR), and this QMS is subject to external assessment for medical devices class IIa and above. For class I devices, you don't need external QMS assessment or certification.
It's not strictly mandatory to have an ISO 13485 certificate, but your QMS will be assessed as part of the conformity assessment, independently of any ISO certification. Many manufacturers choose to get ISO 13485 certification first as a sort of rehearsal—failing the ISO audit doesn't have regulatory consequences, so it's a safer way to test your system before the actual conformity assessment.
As for Switzerland, if your company is based in Switzerland and you want to place a CE-marked device on the EU market, you'll need an EU Authorized Representative right away, since the agreement between the EU and Switzerland is not finalized. Your device also needs to be registered with Swissmedic, and you must meet local Swiss requirements for vigilance reporting. The Swiss MepV is almost a copy of the MDR, but always check for any specific local requirements.
Also, keep in mind Switzerland's language requirements for labeling and documentation.