Hyper-V Server SSD vs NVME M.2
Solution 1:
TLDR No.
It's common to install the hypervisor OS on a low tier/inexpensive disk and run VMs on fast local (like NVMe) or remote (NFS, iSCSI) disks.
Once Hyper-V has loaded everything it needs to run into memory you will not use the disks for much, basic logs, events, etc. IO workload for VMs should be on your faster disks.
And since you're learning, don't forget backups, off-site preferred.
Solution 2:
Something for you to understand, this place is for professional sysadmins and system designers, one of our core objectives is to maintain data integrity and service. Some of the ways we do this is via redundancy and resilience throughout the system. There's a couple of ways we do this, often we buy servers with CPUs, memory, storage and networking that's designed to get by in the event of issues that would cause service outages on more general purpose PCs - these include things like redundant power supples to support loss of power or failure of the power supply, ECC memory that can still work in situations that would fully fail on lesser hardware and data integrity systems such as RAID/erasure-coding/off-site-backups etc.
I tell you this because you're new to this game, we have a lot of people come here that are in exactly the same situation you're in, new to the game and will little resources assigned to you to work with - it's very common - and we try to help where we can.
Now we can't 'magic' up a budget for you to buy server-class hardware but we can help you to choose parts and configs that will serve you well, which you can then go off to seniors to ask to fund. We can obviously help with configuration help to get things going and help tune things to be most efficient.
Again sorry to 'go around the houses' on this one but let's get to the 'meat' here. First of all I would say that the real-life performance difference between regular SSDs (presumably you mean consumer SATA ones?) and NVMe (again I'll assume you mean PCIe) drives are often quite similar - it really does depend on the need for the extra bandwidth the NVMe drive might offer and the level of concurrency needed by the server (as an example often simple gaming PCs see little difference between SATA SSDs and NVMe PCIe M.2 drives). But what I would advise you to do is use some form of RAID to allow for your system to deal with hardware failure. The other aspect involved is 'write-wearing', often servers can 'kill' consumer flash memory remarkably quickly, you need to understand your storage needs in terms of writes and make sure your storage system will not be driven into the ground by these needs.
I'm hoping this has been benefittial, I didn't want to provide a simple glib answer as that wouldn't be much help for you. If you do want a quick answer then I suppose 'don't worry about that side of it, worry about getting RAID (and probably some form of backup too) instead" would be it.