certain diawa's are made for surfcasting, they'll have a very wide and long spool made so the line will easily come off. there are a couple of models in the Emblem Z series that are excellent surf reels.
An ugly stick will work fine with conventional or spinning gear. As for the ugly stik/graphite debate, an ugly stick has a slower action than graphite, more of a fiberglass feel with less snap to it. Graphite has a faster action to it and usually more backbone. Advantages to the ugly is that they are basically indestructable. depends on what feel you like.
as for reels doing double duty, for the most part the reels can easily do both surf and bay fishing, just switch rods.