Are there any general chemical rules for choosing initiators for a polymerization reaction?
It's been my experience that initiators are chosen for: 1) initiation temperature, 2) solubility, and 3) cost.

1) Initiation temperature - Most radical initiators are stable at room temperature; they need to be heated to dissociate. For example, the half-life of benzoyl peroxide at room temperature is very long, but it is about 30 minutes at 92 &deg;C and 1 minute at 131 &deg;C. However, some monomers boil or decompose at temperatures lower than those temperatures. AIBN (azobisisobutyronitrile) decomposes above 65 &deg;C, so less heat is needed. Both benzoyl peroxide and AIBN are suitable for bulk polymerization of most monomers, including acrylamides, acrylates, styrenes, etc. 

2) Solubility - Benzoyl peroxide and AIBN are soluble in organic solvents, which include most monomers for bulk polymerizations. However, if you want to perform your polymerization in water, for example if you are doing an emulsion polymerization, then you need a water-soluble initiator, like a peroxodisulfate salt.

3) Cost - Every initiator has a price, even if you are only using tiny amounts. AIBN may have a lower activation temperature than benzoyl peroxide, but AIBN is also more expensive. There are other more specialized inhibitors that are even more expensive.