What is the difference between 种类，类型 and 品种?
They can all be translated into English as variety or type. Their differences are:


種類


Has a slight emphasis on the differences between compared things, and it is slightly more often used to construct categories to sort different objects into.
Also occasionally used as a synonym for 種族 (race or ethnicity) in older texts (pre-Qing).
Example from Pleco: 不同種類的刀具 (different kinds of knives)

類型


Has a slight emphasis on the similarities between compared things, and it is slightly more often used to group things which share similar properties into the same category.
Sometimes used as a word to categorise tropes, imagery, or genres in the field of literature.
Is a term imported from Wasei-kango.
Example sentence: 魯迅 《偽自由書ㆍ前記》： “然而我的壞處， 是在論時事不留面子， 砭錮弊常取類型， 而後者尤與時宜不合。” (Lu Xun: "My problem is that I don't spare any sensibilities when discussing current affairs, and often use literary tropes when criticising harmful traditions; the latter may be extremely inappropriate in contemporary society.")

品種 


Very often used in the field of biology for the meaning animal breed, species, bacterial strain.
Otherwise used to describe the assortment variety of products e.g. in a shop.