I did Adams glacier route about two weeks ago, it's heavily glaciated, not heavily trafficked but probably more advanced than you would be comfortable with. I wouldn't advise is as a first glacier route, you'll want to know how to climb on a rope team, crevasse rescue, steep hard snow, some front-pointing.
The south spur is a hoot, I went mid-week once and our party of 6 was the only one on the lunch counter. I did it once on fourth of july weekend, it was a friggin goat rodeo.
Baker is supposed to be good but one person told me if the weather is lousy in only one place in Washington, odds are it'll be on Baker. He's been weathered out more than once.
My vote: Adams South spur, up on Thursday, summit Friday morning then hike out.