Plaintiffs' lawyer Ron Miller has an informative post explaining why he serves interrogatories at the time he files a complaint, noting in part--
The advantage in first obtaining answers to interrogatories is that the answers should help the attorney determine who should be deposed, what questions should be asked of those deponents and what documents should be obtained in the case. Having the interrogatory answers, in some cases, also may tend to shorten the length of time required for the deposition. A possible advantage in taking the opposing party's deposition before serving interrogatories is that the party's deponent will not have thought out the factual and legal position thoroughly with the attorney and be as prepared as he/she might be otherwise.
As Miller writes, there's a split of opinion on this issue among plaintiffs' lawyers. The full post, which contains much additional discussion, is titled "When to Serve Interrogatories?"
Related post from Trial Practice Tips: "Depositions Before Interrogatories?"