Hi,
since you do not have a shared storage among the 3 servers, the external Veeam server is going to use network mode, but based on your production design, it does not mean it's going to run bad, it all depends on the amount of data you have to backup daily.
I would personally, in this situation, install Veeam as a virtual machine on ESXi4, connect the MD1000 as a repository to it, and do all the backups of the other 3 servers' VMs. If after some tests backup speed would appear to be slow, I would add additional Veeam proxies directly inside the ESXi servers, maybe installing it on existing Windows VMs to save on licenses.
About the raid, obviously a Raid10 would be the best solution for performance reasons, it will give you fast backup and most of all fast restore speed. In Raid10 your storage would be around 7 Tb, plus a spare disk. If this size is not going to be enough (again, it depends on compression settings, dedup settings, and most of all the amount of retention points) I would use Raid5.
Luca.