In addition to all of the advice being given...

I'll put in the good word for so called "swept" or "north road" style handlebars. Some types to consider, just to get the picture of what I'm talking about:

Origin8 Citi Classic
Velo Orange Tourist
FSA Metropolis

(I have all three on different bikes). Relatively few bikes are furnished with these, but you can upgrade from a flat bar bike, typically without having to replace the controls. In some cases you might have to get longer cables, but that's less of an investment than totally new controls. So you can try the hybrid, with a relatively inexpensive upgrade option in case, like many people, you don't like flat bars either.

For me, rotating my hands eliminates the wrist pain, even when riding in the same hand position for 10's of miles.