Hi krokotiili,
I work for a VMware service provider and Veeam partner so have some knowledge of the challenges you are facing.
As Tyler said, your access to the VMware infrastructure is going to dictate the best solution. If this is vSphere based hosting and you have access to the hosts and vCenter you can set up Veeam as you would with on-prem VMware. If you don't have access and / or the environment is VMware Cloud Director based then your only option is going to be Veeam Agent based backups. In the second option, the service provider can deploy a multi-tenant backup solution integrated in vSphere or Cloud Director but the end customer can't. If this is your situation and the provider doesn't offer a backup solution I'd suggest asking them some pointy questions.
Regarding placement of the VBR server, if your critical infrastructure is running in the hosted infrastructure I'd be tempted to keep the VBR on-prem and deploy proxy servers in the cloud environment to take care of data movement. The VBR will only be the control plane in this design and the bandwidth requirements will be minimal. Should your critical infrastructure be unavailable, you still have access to your backup system and a copy of your data if you put some thought into your repository design. If you suffer an outage in your on-prem environment, only your ability to back up is compromised and if you take a periodic VBR config backup and store it offsite you can recover the VBR into the private cloud to recover from this situation.
When planning where to put your data you need to consider Veeam's best practice 3-2-1-1-0 rule along with data locality and cost (
https://community.veeam.com/blogs-and-p ... p-rule-569).
Option 1.
If you have high bandwidth / low latency from the private cloud to an object storage provider, i.e. you're hosting in a hyperscale provider or in close proximity to a specialist provider's POP, such as Wasabi, I would look to store your primary backups there. These are the backups you would use first to restore service so they need to be the most up to date and fastest to restore. You can then do copy jobs from this repository to your on-prem repository and then off to tape if you wish (you can meet the immutability "1" in the rule with relatively short term immutability on the object repository and / or with a tape copy - I'd be tempted to do 30 day immutability on the object storage plus weekly tapes for log term immutable copies). Watch out for egress fees when planning this however.
Option 2.
If you don't have good connectivity to an object storage platform, a repository running as a VM in the private cloud may be an option but you need to get this hosted on physically different storage to your workloads. If it isn't obvious how you can do this, ask your provider. Again, use copy jobs to get a copy of this data either to on-prem or elsewhere and make sure there is some immutability in use somewhere.
I hope that's useful and provides some food for thought.
Chris
