Volpetti/Mercato di Testaccio vs Mercato Esquilino

We arrive at 9:00a at the Termini station but our apartment near the coloseum won't be ready till 10:30a. As we need to buy some groceries I thought we could do it during this time. We could take the Metro and go to Volpetti/Mercato di Testaccio Markets which I hear is really good.....trouble is what do we do with our luggage (though they should be carry on bags) while we grocery shop. We can then take a taxi to our apartment 7 minutes away. Or do we go from Termini to Mercato Esquilino near Piazza Vittorio, store our luggage at Termini (where do you do that?) and then take a cab....which will be more expensive... to our apartment.
Also would the second option take more time?

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