I personally would just check a bag. Even if take the barest of essentials, it'll be tough (if not impossible) to fit everything into a carry-on size. You also have to take carry-on restrictions into consideration: you won't be able to take anything sharp, any liquids in more than 100mL containers, etc. So no tweezers, nail clippers, perfume, and other things you probably want to take. Yes, you could buy all of that in Sweden, but I found things like that to be much more expensive in Scandinavia than at home (Canada).
Real hiking backpacks (60+L) are expensive and a large pack without an internal frame will kill your back. If you're going to be more or less settled, like studying, I found a good suitcase with wheels much more reasonable to deal with. Buy a good daypack (25 or 30L), as you can easily fit a weekend's worth of clothes into that if you want to travel for a weekend and they're small enough to use every day.
As far as what to bring, dresses are fantastic. They take up almost no space but you can really change up your looks: wear with flats and a cardigan during the day and throw on heels and jewelry if you're going out at night. Same for skirts: a couple of skirts, tops and a jacket and cardigan will make outfits for a week. Comfortable shoes are a must, as you'll most likely be doing a lot more walking than you normally would at home. Jeans are bulky and take forever to dry, which isn't great if you're doing laundry at a hostel. You might want to bring a bath towel if you can't guarantee that you'll have one when you arrive--it's an essential and not all hostels have them. And you'll want a shower after flying forever!