I really believe 3-string sweeps (like Hammett's solo in "Lepper Messiah") are the easiest to begin with , cuz you don't do so much sweeping with your pick ... But there are 3-string sweeps which are very complicated too , I realy recomend "Lepper Messiah" solo or something similar for a sweep beginning.

It worked for me this way , after mastering 3-string sweep I went to 4 , 5 & 6 string sweeping ... It just takes time to master.
BTW, I've seen people who can sweep on 6-string & can't do a simple 4-string ... I realy recomend taking it as stairs 3 , 4 , 5 then 6 strings.

"Speed Kills" is realy awsome , but it can be so FRUSTRATING for someone who isn't used to this kinda stuff yet.