This is a very good question and there has been a lot of debate when it comes to software. FAR 37.101 Service contract means a contract that directly engages the time and effort of a contractor whose primary purpose is to perform an identifiable task rather than to furnish an end item of supply.

You stated this will require software engineers to develop. This sounds like a service, but the end result is a software application, which does not sound like a service. Look at DFARS 208.7401 Enterprise software agreement means an agreement or a contract that is used to acquire designated commercial software or related services such as software maintenance. Here it looks like the commercial software is a supply item, it is already developed.  In your case it needs to be developed so it sounds like a service to develop the software application.