Getting to Manhattan won't be bad. You just take the 7. It will probably take 20-30 minutes the most. Corona isn't a bad area. It does have some problems with poverty. Overall though it's a working class neighborhood, heavily populated with Latinos from all over Mexico, Central and South America. It's not dangerous. Just be smart. I'm in the area often. There can be gangs in certain parts of Corona, as anywhere in the city, but again just have street smarts (don't walk around by yourself at 4am) and I dont think it will really be a problem for you.
Have you checked out the area yourself first? good luck with the move!