NAS for running about 16 virtual PCs

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Thanks for reaching out! Running 16 virtual PCs, especially for resource-intensive tasks like Adobe Flash, requires a robust NAS. Given your budget and requirements, I'd recommend checking out the Synology XS series, particularly the models with Xeon processors. The DS3622xs+ or DS3621xs+ could be solid options, providing the necessary power for smooth virtualization. With your fiber-optic speeds, remote access via TeamViewer should work well. Just keep in mind that resource sharing across virtual machines on a NAS might result in a fraction of the performance compared to individual PCs. As for updating resources, it depends on the NAS model and software used for virtualization, but generally, it should be manageable.
https://nascompares.com/nas-builder/