About my layoff

Hello all:

I was notified that I got lay off, and my last day is end of June.
What should I tell agent or HR if they asked me "Why you want to leave current company"? Directly tell them that I got lay off? If I tell them that I am looking for a better job, I doubt anyone would believe me.

Also, as my last day is end of June. When is the proper time that I should apply for unemployment insurance? 2 weeks before my last day or now?

Thank you in advance