I have 15 years of experiencing optimizing the performance of websites and assembling digital strategies for companies of varying size. I do not currently work with any legal websites, but I do a great deal of work with lead generation businesses which are similar from a web functionality perspective.
When working with clients I typically begin by examining the flow of site traffic after they arrive. For example you may find that visits from LinkedIn, Avvo, and Yelp convert at different rates. This sort of thing can help determine how you spend money to bring traffic to the site.
Examining the "acquisition layer" -- how people arrive on site and what they do immediately upon entry -- is often more effective if you look holistically at site performance and entry channels. Organic, Social, Paid, Rented channels will all typically perform slightly different and you'll want to identify the right mix and the right visitor workflow before blowing through the ad spend.
Your monthly budget is somewhat thin for competitive terms in competitive markets but may be sufficient to run something content-driven with an advertising recon component. Law firms often have significant restrictions on how they advertise so this may play a role as well.
Please call me with any follow up questions you may have. I can help get you started on an effective path.