Finding a job after redundancy

I'm being made redundant due to a company sale, but they want me to work a 4 month notice period as my work transitions to the new company.

I'm feeling a bit anxious about finding a new job after I leave. I see jobs I want to apply for but with such a long notice period I don't know if I should be actively looking yet. I've also never been through redundancy so I'm not sure what I'm allowed to say on job applications.

My work offers enhanced redundancy pay so I'm getting a good payout, and I'm really conscious of protecting that while also protecting myself.

If you have been through redundancy, what was your time frame for looking for new work? What am I allowed to tell people?