We have a tendency to look at business cards from a purely functional point of view, and this is a major contributor to the blandness that is inherent in the vast majority of business cards that are out there. It is important to recognize that aesthetics and function tend to go hand in hand, and you need only look into the differences that serif and sans serif fonts can make on the efficacy of your cards to see the truth in this once all has been said and is now out of the way.
The global trend for what fonts were used on Metal Business Kards has shifted away from sans serif variants, and serif fonts like Times New Roman are therefore becoming more prominent than might have been the case otherwise. The reason behind this is that serif fonts tend to have quite a nostalgic vibe to them, one that your card recipients would respond very positively to. Sans serif fonts are now perceived to be too sanitized and devoid of true character. Your business needs a brand, and this brand needs a personality so you can plainly see what the right option is in these situations.
Utilizing serif fonts in your cards can allow you to give your business a sense of permanence and traditionalism. This is in stark contrast to the almost antiseptic vibe that sans serif fonts have. That said, try not to use default fonts like Times New Roman. Purchasing a custom font can help you to distinguish your business and give it a unique type of personality, and as long as that font has serifs it will definitely do a lot of good for you.