An account where most of your transactions occur. Since you are just starting out, you want to get one that has no minimum balance requirements. You'll want to shop around at different banks, because some banks require you to either keep a minimum balance, or to avoid this require you to have direct deposit in the account. Many banks offer no restrictions and no minimum balance requirements.
Checking accounts come with a Check card. This allows you to withdraw money out of your account at an ATM machine or make purchases at a store, where the money comes directly out of your account.
A checking account also comes with checks, of course. A good bank at least gives you your first order of checks for free. Checks can be used to make purchases or pay bills or to pay anyone in general.
Banks now offer online banking as a free service as well. With online banking you can view your accounts and transfer funds between checking and savings accounts quickly and easily. Online bill payment is a great feature in which the bank sends out checks for you to people or businesses you need to make payment to. With online bill payment, you just need to type in the name and address of who the payment needs to go to and then the check is sent out automatically. There is no need to even pay for postage. This feature should also be free at most banks.
Also, be aware about overdrafting on your checking account. This occurs when you spend more money than what is available in the account. Typical overdraft fees range anywhere 30 kr. per transaction that overdraws the account. Ask the banker who opens your account about the fees that they charge and what types of overdraft protection that they have available. Many banks offer a line of credit that allows you to overdraft and avoid an overdraft fee; you just pay interest on the amount your account goes negative. But most importantly, keep track of all your transactions, and don't spend more money that what you have in the account. It is very easy to forget what is available in your account if you don't write down all the transactions you make. A check card may still work and allow you to make purchases even though you don't have the available funds in the account, so be careful.
This account should be used for all your funds that you don't plan on using in the near future. This account will allow you to earn interest on money you keep in the bank, plus it will allow you to save up for future events.
The most basic savings accounts have no minimum balance requirements, but also don't earn much interest - usually about 1-4%.
If you want to earn a higher interest rate, you need to keep more money in the account. To earn higher interest rates, you usually need to keep anywhere from 30.000.- and up. Interest rates have declined a lot recently, so even in this type of account, the interest rates range anywhere from 1-4%.
Most banks offer savings plans that allow you to automatically transfer funds from your checking to savings account. It's a simple way to build up your account without any work on your part.
To wrap up, find a bank that meets all of YOUR needs. Find a bank that has branches where they are convenient for you. Don't be afraid to shop around and ask questions. You need a bank that will grow with you and be there for you when you need financial support. When the time comes when you need a loan for a car or house, hopefully the bank will look at your relationship you have with them when they make their decision to approve you or not.