I looked at the sightseeing pass last year but determined it would be a bad purchase for me. I bought the weekly transit pass and concentrated all my city transit usage in the last 7 full days of my 12-night stay. I only did a bit better than breaking even as I recall. Stockholm is a particularly pretty city, and I preferred to walk.
Transit is definitely needed for Millesgarden, and most people would use it for eastern Djurgarden--if they're interested in museums located beyond the westernmost tip of that large island. For other sights, your hotel location will be important. There's also the question of how you feel at the end of a long day of sightseeing. Are you more likely to say, "My feet hurt; let's grab a bus or the Metro" or "Ohh, more nice buildings; let's walk that way"?
For summer trips in northern Europe, I pack so I'll be comfortable at 50F on a rainy day. I'm cold natured, so that means a pair of light merino wool long johns (though the upper half is rarely used), at least one pair of nylon slacks that sort of shed water, a light fleece jacket, a waterproof rain jacket and waterproof shoes. On the other end of the spectrum, the temperature could get up into the 80s. Most of my tops are lightweight cotton.