Hi feargalr,
As per your points,
- Set up new virtual machines and install OS's onto them, select how many cores/RAM/Storage space will be available to each VM etc.
Yes its possible to do that.
- Clone virtual machines (this isn't a must but it would be nice)
No, That's a feature in vCenter.
- Take snapshots of the virtual machine (Again would be nice, not a must have)
Yes, Works without vCenter.
- Manage priorities with virtual machines (i.e. set it so that one VM will take priority over another for cores/RAM)
Yes, It depends on how you manage your Limits,Shares and Reservations.
- Connect to ESXi over a network connection to turn on/off VMs.
Yes, as far as you can connect to your ESXi host's subnet and SSH is enabled on the host.