What is the best Rear Derailleur for single speed to 3 speed conversion I am converting my Sonders eBike from a single speed to a three speed and I need some help finding the best Derailleur. I would like to use a Shimano Altus as I understand that they are a step up from the Tourney line. My rear freewheel cogset is 16,19,22t and my front chainwheel is a 48t. This gives me the same speed ratio as my original when I'm using the 19t rear cog. The original chain is 1/8" and I believe that my new chainwheel is also 1/8". My derailleur uses a SunRace Shimano Compatible Index Hanger Plate. The question is, do I use a short, medium or long cage and what is the model number? Thanks for your help, I am converting 2 of these bikes and would like to only buy the parts once.
Yes - Altus are a step up from the Tourney lineup, but is considered a very entry level MTB product. I would encourage you to consider a higher spec model if you can afford it - I suspect the price difference will be small if you shop around. 

Derailleurs are rated by the capacity and maximum tooth size. As you are run a x1 setup, you capacity requirement is 22-16 = 6, and the maximum tooth size of 22 is smaller than a typical road cluster, so any derailleur will do the job. As such, using a short cage will give better performance. 

You don't say what spacing the three cogs are - If you are using an indexed shifter make sure it matches the cog spacing of your cluster. As always Sheldon Brown has all the info you need