She is sort of girl that he would like to get married. -> She is the sort of girl that he would like to get married to.
This is sort of product that will do so well in the international markets. -> This is the sort of product that will do well in international markets.
It is kind of pet that I don’t want to have. -> It is the kind of pet that I don’t want to have.
We put "a/an" after "sort of" or "kind of" only when they're used as fillers or mean “to some extent,” “rather,” or “somewhat.” For example, "It is sort of a difficult task," "It is kind of an easy thing to understand."
However, in these cases, "sort of" and "kind of" mean "type of," so there is no need to use "a/an" after.