Type, kind and sort all have the same meaning and can be used in the same situations:

What type of car do you drive?
An interesting kind of plant.
A new sort of mobile phone.

If you are saying that something is partly true or are not being exact, use sort of or kind of rather than type of:

It’s a sort of oval shape.

Type, kind and sort are countable nouns, and they must be plural after determiners with plural meanings:

a) this type / kind / sort of + singular noun
I don’t like this type of thing.
This kind of mistake is easy to make.
Red wine goes well with this sort of dish.

b) these types / kinds / sorts of + plural / singular noun
How common are these types of illness(es)?
Those kinds of colors look good with dark skin.

Remember to use the plural types / kinds / sorts after all / both / certain / different / many / several / various, among others:

Movies that appeal to certain kinds of people. (NOT certain kind of people)
Many sorts of jobs require computing skills (NOT many sort of jobs)