For travel within Sweden, you may use Resrobot.
In Sweden you may bring your bike without any bike case on SL commuter trains, Upptåget, Mälartåg and most other regional trains. Also, you may bring it without a case on TÅGAB and Flixtrain long-distance trains. On other long-distance trains you have to carry your bike in a soft or hard case.
See the map below, or https://rosnix.net/~per/tag/bike-train-sweden/ (only in Swedish) regarding bringing bicycles on trains in Sweden.
Destination Gotland trafikerar Rostock - Nynäshamn. Färjan tar cyklar av alla sorter (inklusive velomobiler) ombord.
If you arrive by bike you may like to leave luggage at the start. You can use Roadfinder for finding good roads.
If you arrive by car there is parking space at Fyrishov sports centre near the finish. A ticket for multi-day parking can be bought in the parking ticket machine. On Fyrishov there is also a camping site. Remember to rest properly before driving.
If you arrive by air you can take the SL commuter train from Arlanda C to Uppsala.