For a file server, I'd go straight to Azure Files. It's simple and fairly straightforward to deploy - it's far cheaper than standing up a VM too. Probably take a day or so to set up if you're learning it for the first time.
If you want a proper server, I'd just use Azure Migrate to move your file server straight to the cloud. Azure Migrate will right-size it for you during the assessment phase, so you're not paying over the top amounts. Super simple to set up. Probably half a days work starting from zero.
For connectivity, just deploy an Azure VPN Gateway and set up a IPSEC VPN back to your HQ. Loads of scripts for this - can always share the one I use for doing the base networking if you're stuck.