I haven't used MDO for a cabinet, but it would be my first choice of material if I was planning to paint. I like the fact that it is lighter than MDF, more rigid, and more water-resistant. In my case, I'd probably use T-molding for the edges, so they wouldn't be a problem. If you want to paint the edges, I'd probably seal them with glue size or primer before applying the paint. FYI, some companies sell pre-primed MDO, which makes painting even easier!
I'd so some tests with MDO and a router before you commit to routing the edges. The MDO that I've seen doesn't have as many plies as, say, Baltic Birch so it may not route very cleanly. My guess is that you'll need to use a very sharp router bit to get good results.