I had android for smartphone, and didn't like it. I had blackberry, and I liked that one. Now I have windows mobile, and I hate it. I want to design my own OS that I can have a dual boot with my current phone. But which Linux to start with ?

Assuming you have the ability to boot your own unsigned code on the phone (I.E. have something like ClockworkMod installed), you could technically start with any distribution that supports ARM and build from that.

Of course, the Linux kernel is not optimized for smartphones nor does contain support for the proprietary hardware in most phones (which is why the Android kernel forked off of the main Linux kernel in the first place); and using it as an actual phone from within Linux is more or less impossible. But you could certainly boot Linux and play around with it.