Personally, I would recomend an iPod. Since you do a lot of exercising, I would recomend the Shuffle. Granted, I have no experiece with the newest one, with the controls on the earbud cord, etc, but I have the previous generation, and it's great for working out. I've had no problems with it skipping, etc, and it's small enough that it probably won't get in your way. Granted, you never know what song is coming next, but I don't have enough music for that to be a problem.
You also say you want a screen, which, unfortunately, is something the Shuffle lacks. From my experiece, however, having a screen big enough to watch movies, etc and also being convient enough to workout with are often times mutually exclusive.
Now, I don't know what you have against the newest Nano, but that would be my ideal suggestion for being able to watch movies and workout. If you don't like the shake to shuffle feature, you can disable it. I do a lot of running, myself, and I haven't had any problems with it skipping, or shuffling when I don't want it to.