Do you think goodwill should appear on the new company's statement of financial position after a takeover?

Not compulsorily.  Depends on the purchase consideration.  If PC is less than net value, it can be negative goodwill (capital reserve).

if the cash paid > the net value of assets for the company it should be reported as good will

if the cash paid < the net value of assets for the company it should be reported as gain in the income statement.

Yes, if purchase consideration is more than the value of net assets taken over