There are many ways to deploy the engine. If you want to run the engine without the shared engine configuration that ships with the Camunda distribution, then you can create you own web app and start the engine there. In this case it would probably be better to use a different Tomcat to avoid unknown side effects of using both a shared engine and standalone engine.
If you want to make calls to that engine from a separate webapp - the using the REST API is best.REST API
If you want to reach out from the Engine to the world, then using Connectors is a good start.
Thank you for the answer , Conor.
Connectors are rather complex mechanism.
I tried their API - it is not simple, docs are not descriptive regarding
connectors, examples - complex.