I work for an early stage professional services app startup. How should i think about conducting market research, given our space?

In my response, I'm assuming your company will be selling to professional services firms. I'd start with these questions:  

• Where are the dollars spent for professional services? What are the segments/industries/geographies/largest firms?
• Who is serving those segments? How are they solving the problem your app solves/will solve? Also think about how firms are solving the problem today (spreadsheets/DIY/manpower).
• Are there significant markets not being served by alternatives? Why?
• For markets being served, what do users like or dislike about current offerings on the market (primary research and reviews)
• Who are the user and buyer personas? What problems do they have? Are they willing to pay for a solution to their problem? Where does the problem you solve align with their order of priorities? (primary and internet research)