Large external HD array for a Mac mini with RAID to run the Mac mini as a NAS I'm looking at getting a NAS to store about 12 TB of data (but would like expansion options in future).

The main purpose of the NAS would be to: 


Backup 
Have cloud files like Google drive and Dropbox.
Backup our laptops (Time Machine).
Store archived project files (live project files would still be kept in Dropbox).
Possibly work directly on files on the NAS with at max 10 people working at any one time. 


Additionally, I would also like RAID options for redundancy.

I've been looking at some Synology NAS models, which can do the above, but they seem to either be reasonably priced but using an Intel Atom CPU. Or quite expensive but using an Intel Xeon CPU. I see there is no option for a Intel Core CPU, and I'm concerned at the unit being under powered with an Atom CPU.

I have a 2012 Mac mini with a i7 CPU c. 2.5ghz which is a decommissioned work machine. The hard drive in side of it is too small for the tasks above, but is there a way I could attach a large external drive array with RAID via USB 3 and run the Mac mini in Server mode to accomplish what I want to do without buying a Synology NAS?
I have a 2012 Mac mini with a i7 CPU c. 2.5ghz....is there a way I could attach a large external drive array with RAID via USB 3 and run the Mac mini in Server mode to accomplish what i want to do without buying a Synology NAS ?


A "large" enclosure?  No.  The biggest USB 3 Direct Attached Storage device I've seen was a 5 bay unit made by Drobo (I won't have those anywhere near my data centers because of their reliability issues).  Can you expand them?  Sure, by purchasing another enclosure.  As long as you have free USB 3 ports, you can add another unit.  

Promise makes the Pegasus 3 Thunderbolt RAID enclosures that can hold up to 8 drives but they're horribly expensive.

So, (IMO) DAS really isn't a cost effective solution in the long run which, ultimately means the Mac mini isn't a great file server to begin with.  Additionally, macOS also lacks critical support for things like iSCSI making it a poor choice for a storage server.

I would go with the NAS as it's much more cost effective, feature rich, and flexible.  To the contrary, running macOS (an OS more oriented to the desktop rather than a server) just adds way too many layers of complexity to your storage equation.