One big consideration is how much actual work is the construction company doing themselves and how much are they sub-contracting. If they are sub-contracting a lot of the work, who is going to be involved in choosing the sub-contractors? As the owner do you have any input or decision making ability or do you trust the company to make the right choices?
What is the construction company prepared to offer with regards to assurances for sticking to the construction schedule, informing you of delays, or having options for handling problems or difficulties that arise in the construction? Discuss these questions with the professionals.