If your company is a C Corp (filing Form 1120) it does not matter whether you file your business return or personal return first. If, on the other hand, you were an S Corp (filing a Form 1120-S) or a partnership (filing Form 1065), you would need to file your business return(s) first. That's because an S Corp and a Partnership return generates Form K-1s that are needed by the shareholders/partners in order to prepare and file their personal returns.
[Edited 03-26-2020]
The 2019 filing deadline for Form 1120 has been delayed until July 15, 2020.
