Yeah, doing some basic mountaineering training like Gene said would be pretty smart. For Rainier and Fisher you should also have your crevasse rescue systems dialed and glacier travel knowledge. That said, if you spend a day practicing self arrest and another day practicing crevasse rescue you will be fine and should be able to do all of those routes no problem if you've been cruising around the High Sierra already.
Since rock climbing is something you're already experienced with I would not shy away from routes with more of that in them, but it sounds like you want to spend time trying the more snow/glacier type routes and build that experience.
Other glacier mountaineering objectives to consider besides Rainier and Shuksan... Baker, Adams, Glacier Peak, Olympus. Honestly I would just pick whichever one is closest to you and try do multiple routes on it.
Rock(ier) routes to look at that still have some of that... Southern Pickets like Inspiration have a good little glacier to get across, other routes in Boston Basin.
Don't get too locked into specific routes. If you have a chance to go with a solid partner or get on the right type of terrain, just take it.