Which material tends to resist current by catching freed electrons to fill their valence shells?

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The material described is an insulator. Insulators keep their electrons tightly bound to atoms, with a large energy gap between the valence band and the conduction band. Because there aren’t many free charge carriers, current is hard to sustain. If electrons are ever freed by a strong enough field, they quickly recombine and are drawn back to fill the valence shells, so the material tends to resist ongoing flow.

Semiconductors have some freely moving carriers under the right conditions, so they conduct more than insulators. Dielectrics are insulating materials that store charge mainly by polarizing in an electric field rather than by letting charges move freely, but the idea of electrons being recaptured to restore stable valence shells aligns most with insulators. Conductors have plenty of free electrons, so they readily conduct.