grammatical number - Does "a [x] of [y]" take a singular or plural verb?

What kind of verb, singular or plural, goes with phrases like "a record of [singular or plural noun]", "the use of", "the time of"? Does the choice depend on the following nouns (a record of nouns) or on the 'first' nouns (record, use, time)? Or do these phrases obey the rule of proximity (as does "a variety of")?

I have found different example sentences on the internet (source: newspapers or magazines) with different uses. What is correct?

Examples:

• there were a record of other issues;


• there were a record of 28,000 runners;


• there was a record of these statements.