What should I do right after arriving in Sweden?
First up, get yourself to Skatteverket to get your Swedish Personal Number ("personnummer")—this 12 digit number will be your VIP pass to life in Sweden. Read more about how to get it, other alternatives, and how to book an appointment in this Guide: How To Get A Swedish Personal Identity Number.
Next, try to sort out permanent housing (or somewhat permanent like a mid-term rental) if you haven’t already, and get your hands on a Swedish bank account and phone number. Once all that is sorted and you're ready to blend in like a local, sign up for SFI (Swedish for Immigrants) classes, download Duolingo or ramp up your Google Translate game, and start tackling the Swedish language—it’ll make life in Sweden a lot easier (and more fun).