With potentially 16 partitioned wired network spaces, will I need a router with that many ports?
Not going to discuss actuals products, but...
You don't need a router with a large number ports if you use a decent L2/L3 switch between the gateway router and their internal gateway devices...
eg, the building has an IP range of 9.1.1.100/27. For example each business is on a separate floor and each floor has it's own dedicate global addressable IP from the 9.1.1.100/28 pool. You simply need a switch between the building router and each floor (each floor gets its own port on the switch).
Why does this work... well the switch (either via VLAN or ARP) will only forward frames to the correct floor based on IP... And to the building router, it only cares about that on one side if 9.1.1.100/27 and the other is the rest of the world...
So:
10.0.0.0/8 -> NAT device (internal gateway of business 1) 9.1.1.103 -> switch
10.0.0.0/8 -> NAT device (internal gateway of business 2) 9.1.1.104 -> switch -> building router (9.1.1.101) -> The world...
10.0.0.0/8 -> NAT device (internal gateway of business 3) 9.1.1.105 -> switch
Note that this is simply one way of doing it, as you mentioned you could get a 16 port router and each internal gateway device connects directly to one of it's ports... The only time that this would be required is that each internal gateway device has a globally routable IP address that is not with a common small subnet address range (like in my example). But if the plan is to sub-let, and you're providing ISP service, then they get the IP address you assign them...
The other way, is just to NAT them behind the building router, and they need to get permission to have inbound ports open... but this is messy for obvious reasons.