I voted bridge camera. I have a FujiFilm Fine Pix S5200.
I like it alot but it does have limitations that I wished it didn't have, such as lack of great shallow DOF. It does have an awesome large DOF, though. I also want a camera that can accomodate a faster lens for those low-light, kids-never-stop-moving shots. Otherwise it is a great camera. The manual controls lets me learn the basic concepts of photography while saving money up for the DSLR I want.