Using an external harddrive to store games

Drive speed will only affect loading times, not performance, since games try to avoid reading from disk during game play.
I guess that loading times may be around twice shorter or more on an SSD. It all depends on how much you are willing to pay to get shorter loading times.

 

The time to join a server depends on the network, not your drive speed.
I was referring to the loading of a level, but this also applies to launching the app (though you don't do that very often).

 

HDDs are bigger and cheaper and work fine for external storage of games. I assume you know how to set up an additional steam library on an external drive, not difficult at all.