In our environment, we have iSCSI and FC SANs and NFS servers. Here's how they break down:
iSCSI SAN: cheap OK thing if running over GigE, don't expect any magic here; more expensive per port but more performant and easier to implement (a teamed pair of connections instead of 6+ gig ports) if you have 10GigE. If you go with the latter, in just a few weeks you'll have a good selection of HP 8th gen or Dell 12th gen servers that have 10GigE LOM ports.
FC SAN: HBAs are still expensive, switches not so much ($300 per port or less), ridiculously easy to make it perform well (just do nothing).
NFS: useful, but creates some limitations (MCSC is not supported, for example). This is where your success really depends on the quality of the product you buy.
And maybe I'm bending some Serverfault rules here, but allow me to recommend specific vendors (and this part is really very subjective, so please don't flame me - I'm sure there are other equally good or better products).
First, VM storage: Tintri. It's a SSD/SATA box that provides NFS based storage for vSphere environments. They don't do anything else. We have two of their units, and this is the holy grail for an overworked admin who doesn't want to spend time managing storage. Once installed, their systems don't need any attention whatsoever.
If you do want SAN, EMC has finally seen the light, and their VNX/VNXe product lines have more reasonable price tags than the older hardware - as long as you don't ask them for advanced software capabilities. But you can't go wrong buying storage from VMware parent company.
Second, backups. I see one standout company in VM-specific backup space: Veeam. Again, they focus on VMware (lately Hyper-V too), and their approach checks all the boxes you have, including restoring specific files from VMs. They achieve it by enabling the administrator to restore a complete VM in a sandbox and then pulling whatever data is needed from that VM, manually or with some helper wizards in case of Windows file servers, Exchange, or AD servers.