A good checking account will have (ranked in order of subjective importance):
No fees, particularly monthly maintenance, incoming wire, etc
ATM Fee Reimbursement: ATM fees from other banks are reimbursed
Convenience- A clean website, 24/7 customer service, and mobile banking
High Interest Rate- Any non-zero rate from a checking account is nice
Security: FDIC Insurance and a secure website
No minimum balance limit
Once again, Ally Bank offers a checking account with all of these important features. If you rarely use credit cards, open an Ally saving account and never worry about finding your bank's ATM again. Every ATM is your bitch now.
What About Credit Cards?
People often use the same bank for their checking account and their credit card. Banks encourage this by giving exclusive perks for having a checking account, but you don't have to use them. If your bank's checking account is inferior, you can neglect it as an Asian father whose son just scored a 96 on a math test would (“What happened to the other four points? Go to your room, no eat dinner tonight.”)
Real world example: Naturally, I prefer to keep most of my cash in the highest-interest account I have, which is my Ally Savings account. I set my credit card to be paid automatically from my Ally Savings account, saving me time and money. I withdraw cash from my Ally Checking account, which earns .4% interest as opposed to 0 with Chase and lets me use any ATM for free, not just their own.
Paper or Plastic?
Credit cards offer all sorts of rewards and convenience and make it easier to spend money. You should have a couple to establish a credit history.
It's much harder psychologically to spend with cash than credit, as cash is tangible. If you’re desperately trying to save, cash is the way to go.*
But if getting a good value is more important to you than saving money, credit cards are for you. Your first card should have no annual fees, as this account should be kept open for the rest of your life to extend the age of your credit history.
Check your credit score so you don’t waste your time applying to credit cards that you won’t get approved for. I will discuss how later, but next, I will mention a better checking account for international travelers.
*Debit card users get the worst of both worlds, spending more than they would with cash, getting few if any rewards, and having to pay the cost immediately rather than getting 27 days to pay it off interest-free.