Ones with interchangeable lenses or point and shoot?

Depends what you are looking to achieve.

Camera with interchangeable lenses are not considered compact models. How much do you have to spend on a camera ?

Need a lot more information about your level of expertise as well as what your intentions are when it comes to taking pictures.

Do you travel a lot?
Is size and weight an issue?
How much do you wan to spend?
Is your question related to image quality or what?