VMware Player does not provide an option to run as service and/or to automatically start VM's when the hosts is powered on. This feature "Shared Virtual Machines" is only included in VMware Workstation.
Running a production VM using VMware Workstation (or Player) - at least in my opinion - is an option in a small environment, where you don't want to spend money on a dedicated ESXi host. The difference between VMware Workstation and ESXi is the type of Hypervisor. VMware Workstation is a Type 2 Hypervisor, which means it runs on top of an OS (Windows or Linux) whereas ESXi is a Type 1 (or Bare-Metal) Hypervisor which is installed directly on the hardware and does not have to rely on another OS which increases reliability and reduces overhead.
André