I second the advice of EugW in reply #15 above.
The "slowness" is not so much the RAM.
It's the platter-based hard drive inside.
Platter-based HDD's can't run recent versions of the Mac OS very well.
Yes, the OS "runs" ... but it feels to the user more like it's "walking".
It's not worth spending much on a 2011 iMac.
Your main problem here is you can't use USB because the 2011 has USB2 (not USB3).
A smaller-sized thunderbolt drive (250-256gb) will do the job.
Even so, these cost more than a USB3 drive of equivalent capacity.
But... for a 2011 Mac... it's "the only way" -- other than opening the case and putting an SSD inside. Not sure if you're willing to try that.
Final thought:
How's your budget?
It looks like there could be a few new iMacs for 2018 on Tuesday (I wasn't expecting them until next year)...
The "slowness" is not so much the RAM.
It's the platter-based hard drive inside.
Platter-based HDD's can't run recent versions of the Mac OS very well.
Yes, the OS "runs" ... but it feels to the user more like it's "walking".
It's not worth spending much on a 2011 iMac.
Your main problem here is you can't use USB because the 2011 has USB2 (not USB3).
A smaller-sized thunderbolt drive (250-256gb) will do the job.
Even so, these cost more than a USB3 drive of equivalent capacity.
But... for a 2011 Mac... it's "the only way" -- other than opening the case and putting an SSD inside. Not sure if you're willing to try that.
Final thought:
How's your budget?
It looks like there could be a few new iMacs for 2018 on Tuesday (I wasn't expecting them until next year)...