For a 2011 iMac with a platter-based HDD inside, you might get the best performance from Mountain Lion (10.8).
With the most recent releases (El Capitan and Sierra), you may find that the overall experience is that the OS seems to be "walking" instead of "running". These OS's seem to have been designed to run best on Macs with SSD's.
One way to get a LARGE performance improvement for a 2011 iMac (it has thunderbolt, right?):
Add an external thunderbolt drive with an SSD inside.
Let that serve as your "external booter". Leave the current HDD inside.
Not cheap, but "fast & easy", and it will breathe new life into an older Mac...