1. Number of Hyper-V 2012 hosts
2. Number of VMs running Windows Server 2012 or Windows 8
3. Hyper-V 2012 storage type (local, shared CSV2, shared SMB3)
4. Are you intended to be testing beta in test, or subset of production environment
5. Are you primarily interested in testing on-host, or off-host backups
6. Your relationship to Veeam (partner, current customer, trial customer)
7. Your region (city and country)
I cannot guarantee that anyone will be accepted for beta, because I do not make the selection. Private beta is driven by Veeam system engineer from the corresponding region, and they are the ones making the selection (usually, there are no more than 2-3 beta participants per region). So, I will simply route the information about all applications to the corresponding sales teams, and recommend that they put you on beta.
I will not comment on specific applications below, but this does not mean I am ignoring this thread.

Thank you!