Get the english
version of "Arholma - Landsort and Gotland" its a perfectly sized book that has a large number of natural harbours in them as well as maps of stores guest harbours tourist attractions etc.
This is a book that EVERYONE has in sweden
and you should get it too if you have time to spend a few days in the Stockholm archipelago.
Remember that "skärgårdsstiftelsen" has placed crude but sufficient sanitary facilities at a number of natural harbours. One thing to keep in mind overall though is that on weekends the number of boats quadroples which can make it rather hard to find a berth at some guest harbours.
But i agree if you want an easy route
go into sandhamn and then just follow the commuter ships from waxholmsbolaget when in doubt. The island oposite Sandhamn Lökön usually space but the area is among the bussiest in the Archipelago so could be full.
Regarding charts Båtsportkortet Mellersta is the one containing the last part of the route into Stockholm. with 2m depth
you can sail past Waxholm on your way in atleast which is highly recomended as it is a much more beautifull setting then the dreary Oxdjupet on the opposite side of Rindö.
Also don't worry about anchoring
in a natural harbour the bottom is mostly clay and depth increases pretty fast at most places where the land ends.
If you sail in on a weekend though there will be alot of sailing boats heading along the route from sandhamn into stockholm so you could just sail behind them to make it easier.