You'll need to look further into licensing. There was a minimum requirement of vSphere essentials for backups, and there were some references in release notes to this no longer being a constraint. So you may still need it, you may not it'll depend on your vSphere version.
Software
In your situation, I'd use vRanger or Veeam for DR, timed replication can be setup for your VM's depending on rate of change and available bandwidth to a similarly spec'ed ESX host.
I'd also use it for image based backups of your VM's, with some additional software to backup to tape (Arcserve, Acronis, whatever's your poison). Veeam can write to tape too, but I don't think it'll help if you want to do agent level backups - someone else may be able to comment there, as I've not used it in years.
You know your customer/friend better, but whether you use agent level backups for exchange/SQL/File is over to you. Image backup is great for DR or where you'll only ever have to restore an entire disk or the entire server, but it's unwieldy for granular restores.
Cataloging in vRanger (I presume Veeam has something similar), can speed up file level restores but I've not tested how good it is, so you'll need to get a trial and test for yourself if it's restore times are acceptable to the customer.
Aaaaand finally, assuming you have AD, don't take an image backup of a DC - use the built-in tools MS recommend. If you have just 1, you might get away with it, more than that and you are heading for a world of pain.
Hardware
Rotor is spot on with his recommendation, something with a nice chunk of storage and the tape drive attached. You'll have vRanger/Veeam and your tape software installed on it - not a great deal more to say about it.
With the compression that vRanger/Veeam provides you probably won't need the full 2.5TB LTO6 can provide. But even if you do, as long as the job timeouts are set sufficiently someone just needs to change the tape when they get in and let the job complete.
This will only be once a week for your full, every other day should happily fit on a single tape.
We backup to LTO3/4 tapes in an HP MSL8096 tape library. We have seperate servers running vRanger and the tape library, but it's otherwise not dissimilar to the setup outlined above.