Rollover from 403b to Roth IRA or IRA?

I have 403b plan with my previous employer. Now I change my job to another university which does not accept rollover. I would like to get advice on rollover to IRA or Roth IRA.

My understanding:
Traditional IRA is before tax and Roth IRA is after tax. The maximum contribution is $4000/year (either traditional or Roth or both together).

Can I rollover to Traditional IRA or Roth IRA? Should I pay penalty? Is there any limitation for rollover (for example, I just can rollover $4000 per year)?

Or, I can open an individual retirement account and rollover all my money to it. Should I pay penalty?

Any suggestion will be highly appreciated.