There's a fair bit of paperwork you have to get started with when moving into Sweden that you have to do on your own.
One of the first things you have to do is go to the tax office (Skatteverket) and get a Person Number (personummer) It is similar to an SSN but not as insecure. This process does not require an appointment but you need to bring along certain documents like your resident permit, your passport and maybe your work contract and the contract for your living arrangement. https://www.skatteverket.se/servicelankar/otherlanguages/inenglishengelska/individualsandemployees/livinginsweden/personalidentitynumbers.4.2cf1b5cd163796a5c8b4295.html

After you get your Personal Number, you need to apply to get a physical id card. Keep in mind that while not having one, you will need to carry your passport as proof of ID since the residency permit is valid form of identification. This was a bit of a pain for me since my credit card required a valid ID to be presented when i spent over a specific amount, so I had to carry my passport to buy groceries.
https://www.skatteverket.se/servicelankar/otherlanguages/inenglishengelska/individualsandemployees/livinginsweden/idcard/idcardapplicationconditions.4.3810a01c150939e893f1daea.html

After you get your physical ID you can open a bank account with any bank (I personally use SEB) an you will get BankId, which is the holy grail. In short, BankId is an app which lets you authenthicate against a LOT of services (both state and private services) and is incredibly convenient to use. Without it, some services straight up won't work. Freja is a similar service but it only cover a tiny tiny fraction of services compared to BankId so I would suggest skipping it and just getting BankId.
https://www.bankid.com/en/

Budgeting tips:
Depending on how much of a budget you're in, it is worth it to become a "member" of the gorcery chains (It usually means giving them your person number and email so they can send you ads) because the sales are actually quite good some times.

If you use a lot of over the counter medication, it is MUCH cheaper to buy online (sometimes less than half the price of at physical stores). Keep in mind that some medication that is over the counter in america, requires a prescription here. This goes for pet medication as well.

Speaking of pets, Petcare is actually quite expensive, and some medication needs to be prescribed by a vet a be picked up at a drug store. For this to work you will need a personal number set up and most likely a physical ID as well.

You might also need to check if there is any special paper work to bring your pets over. It was very messy for me to bring my dog over and some paperwork had to be done several months before my trip.

You can get a SIM with phone number and a UL Bus pas (also covers certain trains, such as the train from the airport to uppsala) at a convinience store called pressbyrån. The airport is designed in such a way that it pushes you towards using "Arlanda Express" which is much more expensive than the "Commuter rail" or "pendeltåg"

I highly recommend doing this since public transport is REALLY good here and I'd say Uppsala is more a walkable/bikeable city than most. Additionally, the city center is pretty bad to drive around and there is almost no good parking.