I believe the current biggest capacity 2.5" drives are 2TB although bigger ones will of course be on their way. With regards to firmware limits 2TB is usually below such thresholds so I would expect a 2TB drive to work fine.
A Seagate Spinpoint M9t 2Tb 2.5" Internal Hard Drive ST2000LM003 would be a 9mm 2TB 5400rpm drive that therefore should fit and work. I do not believe there are any 7200rpm 2TB 2.5" drives as of yet.
As others have mentioned even though your old Mac mini is limited to SATA II which is 3Gbps an SSD drive would still give better performance although not as much as if you had a newer Mac mini which supported SATA III. SATA based SSD drives like the Samsung 850 EVO are now also available in capacities of 2TB and are also thin enough to fit, they are of course much more expensive.
Perhaps you should consider upgrading to a newer model Mac even if it is a second hand one, e.g. a 2012 model i.e. a Mac mini 6,1 or 6,2 which supports SATA III.