procedure of a website redesign – how to get started when redesigning a website

Designers out there who have experience with complete website redesigns. I'm on the brink of starting a website redesign. What procedure is best?

Currently I'm awaiting feedback from the companies strategy and at the same time I would like to do some research with a questionnaire on the current website asking about come from, website usability etc. Is this the wrong time to acquire such research?

How do you guys prepare/research for a complete website redesign?