It is not the size of the firm that matters but the quality of the lawyer. Definitely interview a few lawyers from a variety of firms. Experience in your kind of case is one factor to consider as is litigating against large companies. Also, lawyers speak through their fees. If someone will take it on a contingency, that shows confidence in your case.
While I understand that the size and the stature of the company might make one think that the use of a large firm is necessary, that is definitely not the case. For example, I recently represented 14 condo unit owners who litigated a case for four years against the city of Taunton and two other defendants, and the case recently settled for $1.35 million. None of those defense attorneys thought that my status as a sole practitioner affected their strategy in the case. If an attorney is competent, dogged in his/her pursuit of your claim and makes clear to his adversary his knowledge of the facts, the applicable law and the strategy employed to achieve the best possible result, those factors, and not the size of the attorney's firm, will be relevant.
In my experience, there is never a black and white case of invasion of privacy and you should not bring a claim unless you are willing to go through trial on it. Unless the case entails a huge amount of documents and requires multiple attorneys working on it, a small firm can do just as good as a job. Hire an attorney whom you beleive will do a great job, not someone you hope the other side will be impressed by due to the size of his or her firm.