What are the tools you recommend for deploying / automating / organizing vm in the private cloud
The answer will depend on how much you want to change. I will describe how most larger companies solves this nowadays.

Containerize the apps. Run them in Docker containers. And use a container orchestration tool, like Kubernetes to manage deployment. But to do this your application must probably be redesigned to follow The Twelve factor methodology.

Both Amazon, Azure and Google have Kubernetes cloud services. If you want to continue with private cloud, OpenShift is the most popular Kubernetes-product.