I look at it this way, if I could get an Exabyte (EB) drive to physically fit I would put it in ;-}
The size of the drive physically and the amount of power it requires and the amount of heat generated is your limiting factors here not the storage size. As time has progressed year to year the HD makers have managed to squeeze in more storage in the same 3.5 form factor HD's. Which is why your choices have changed.
Apples OS's (Lion and on up) have been able to access and use drives externally that are much larger than 3TB.
In the same vein the HD makers have also improved the SATA I/O and the current SATA III (6.0 Gb/s) is about to get an upgrade as well.
Sadly, your systems SATA I/O is SATA II (3.0 Gb/s), and yes, the drives SATA speed does matter. To start things here you want to make sure your EFI firmware is the latest for your model. Review this Apple TN it will tell you how to check and point you to the needed files EFI & SMC firmware updates for Intel-based Macs. Then review the HD's specs you are planning on using making sure it can be either adjusted to the SATA II or SATA I I/O speed. In some cases the drive will auto sense the I/O speed in your case being a SATA II system you should be OK with one of these drives.
While your at it I would also max out your RAM in this system to 6GB (1-2GB module & 1-4GB module).
As to OS's: I would stay at the older Lion or Mountain Lion OS-X versions. Mavericks maybe a little taxing on your older system (at least the .0 rev of it now).
Hopefully that answers your Q's