What type of field do I need to insert so that my fill-in Word template will allow a table to be pasted into the form?

There is no formfield into which one can paste a table. You could do so with a Rich Text Content Control, however. Do note that Content Controls are only supported by Word 2007 & later and, generally speaking, shouldn't be used in a document that has formfields.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]

You could create an unprotected section of your template in which the table could be pasted. You could perhaps mark this with a macrobutton field.