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.

We do not put "a" or "an" after "kind of" and "sort of". We use those in case we want to soften other words follow them in speaking rather than category. "kind of" is familiar with American English and "sort of" is familiar with British English. You can find more examples on https://dictionary.cambridge.org/grammar/british-grammar/speaking/kind-of-and-sort-of.

No a, but you need a 'the' before. She is _the_ sort of girl that he would like to get married _to_. This is _the_ sort of product that will do so well in the international markets. It is _the_ kind of pet that I don’t want to have.