First you must decide on what type of properties your polyisoprene must have. Cis/trans affects how much crystallinity which will affect elongation and practically every other mechanical property. I'm assuming if you're vulcanising it you don't want the highly crystalline brittle trans material (gutta percha) but like everyone else who's trying to replicate natural latex, you want a high level of cis. Most vulcanates have a host of other modifying agents aside from sulfur and ZnO (such as lubricating oils and conditioners, reinforcers like carbon black or chalk, and different things to control scorch time).
You can polymerize it radically or with metallics and a host of other initiators.
Source: Direct experience with having polymerized isoprene, worked with latexes, used a Banbury, horizontal mill and gotten very dirty in the process. The rubber industry is a very dirty job!