You might want to just contact iX to find out how many concurrent users the Mini will handle. I'm sure they will know, I just can't find the information in the google box. The FreeNAS Mini is based on an Intel 8 core Avoton CPU apparently, and 16GB-32GB ECC RAM. If a P4 box was fine, this should be extra fine.
First thing I would do while you are busy deciding what to do for the NAS is get a decent, managed gigabit switch in to replace whatever plastic box network gear they are abusing at the moment. If you are trying to do this a bit on the cheap, I've purchased for myself a used Dell PowerConnect 5324 for a good price on eBay, and I am very happy with it. There should be a pretty good selection of decommissioned network gear ripe for the picking.
One thing you can do to really up the capacity of the network is port teaming or link aggregation. To do this you will need more than 24 ports. If the 12 workstations all have dual NICs, you'll have burned through every port on a 24 port switch without even hooking up a NAS. Another thing to watch out for is that there might be a limit to the number of link aggregation groups a switch can handle. For example, my switch will do up to 8 LAGs, even though it is a 24 port switch. If you use two 24 port switches, you can do a 4 port LAG trunk between the switches, a 4 port LAG to the NAS, and split the 12 workstations equally across the switches. Per switch you'd be using 12 ports for 6 workstations and 4 ports for connecting between the two switches. We're already at 16 ports so far. Add 4 more on one switch for the NAS and that only leaves you 4 ports on that switch for the boss, a printer, the internet, and an access point, and 8 on the other for whatever else gets added to the network (pfSense box? more employees? more printers? more NAS? more APs?). Worse yet, it leaves only one LAG leftover between the two switches.
With a 48 port switch, you would eliminate 4 ports on each end for a total of 8 ports freed up, but the catch is you will have to spend more on a switch that supports 13+ LAGs. Looking around a bit, I found Dell and Cisco's sites to be rather unwielding of this sort of information. I didn't find anything helpful regarding Cisco's Catalyst line, and their other small business products seemed to be 4 LAGs max (?I hope I'm mistaken). Dell's products in the fathomably affordable range seemed to give up to 8 per chassis. Furthermore, both vendors' managed 48 port gigabit switches seem pretty pricey, even used. On the other hand, I wasn't even looking and happened to stumble across a table on Juniper's site that showed the number of LAGs supported by each of their product lines. Even the bottom end models will give you 32 LAGs in a box, and I spotted several 48 port options on eBay for around $600 (like this). Juniper is a good brand, so the EX2200-48T-4G looks like a perfect option to me. It will be flexible, reliable, and allow for future expansion, all for under a grand.
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Ah, er, maybe this is getting a bit overboard for your needs :)