follow b_b's advice.
I didn't. I used BofA's college kid account or whatever for 4 years because they had tons of branches in LA and NYC and that made it easy. My dad also had an account with them and so transferring money for tuition or emergencies was/would have been easy.
Then, when they raised their fees and stuff when I didn't have a minimum balance (beware of minimum balances!!!) I switched to Chase because they were easy, the guys in the local branch were super helpful, and they offered to waive all not-meeting-minimum-balance-fees for a year.
I like the ease of bigger banks, even though I hate them. There are ATMs everywhere, they have check deposit on the phone, their apps let you do everything super easily online or from the phone, customer support 24/7, etc. I had some issues with BofA but haven't had any issues with Chase. randomuser always used credit unions and liked them but there can be some issues with ATMs, getting a human on the phone 24/7, etc. if you travel outside your hometown.
Here's my advice for credit cards, if you want to dive into that. I would wait a while...or not do it at all...
Okay so I only got my first credit card about a year ago at the ripe old age of 24. I watched a lot of my friends get themselves into credit card debt, etc and was terrified. The reality is, credit cards aren't terrifying and are a good thing to have and to use as long as you pay them off in full every month. I'm lucky to be dating a guy with good credit even though I, up until a year ago, literally had no credit.
Perks of credit cards:
(1) They are infinitely better to use overseas (especially if you have a no transaction fees one) because the credit card company will fight any fraud battles for you. If you debit card gets frauded, you have to deal with it and fight it. But since the credit card is technically their money, not yours, they fight for it.
(2) Perks - Discover IT and Chase Freedom both have rotating 5% cash back on things like restaurants or amazon.com or whatever. After a while you can cash out or go shopping online which is awesome. It's like free money (AS LONG AS YOU AREN'T PAYING INTEREST ON A BALANCE OR LATE FEES!!!) Go on nerdwallet to see all the shit credit cards give you.
(3) It'll show something on your credit report and help you build credit. All my shitty little apartments in NYC never reported anything to the credit agencies. I had no credit cards. When we were applying to this apartment, I wouldn't have gotten it without randomuser because I literally had no credit. This apparently is fine and expected when you are 18 years old but not when you are 25 years old. :(
I have a checking/savings account with Chase so I have a Chase Freedom card (limit: $1200) & a Capital One Quicksilver card (limit: $300). They give the Quicksilver to everyone with a low limit that can be raised in a year or something so it's an excellent starter card. Added bonus: no foreign transaction fees! randomuser has the Discover IT card too. Discover and Capital One give you access to your credit reports which are good to keep an eye on. You can also use Credit Karma (which is free).
I use my cards for day-to-day transactions and then pay it off in full every month via autopay. I never spend more that ~30% on each card (apparently that hurts your credit score) and never spend more than I currently have in my checking account. I have weekly account balances for all my accounts automatically email me once a week so I stay super aware of what money is where.
So, let's say you open your account and get a debit card. Then you open a Capital One Quicksilver card and they give you a limit of $300.
When you are out and about, spend ~$100 on the Quicksilver card. Once you've reached that, use your debit card. At the end of the month, pay off that $100 with your debit card / checking account and start over. Don't get obsessive about perks and all that at the beginning—all this is going to do is help you have credit in 5 years when you need it for that nice "real" apartment or a car lease or whatever. Once you get good and confident and don't fuck yourself into credit card debt and want to spend more than $100/month, then start researching another credit card. Your credit union might have one or you can go on nerdwallet and find one that gives you the perks you want.