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When it comes to choosing a bank, you have a wealth of options.

After all, there are nearly 5,800 banks in the U.S. and about the same number of credit unions.

Best Banks

Picking the right financial institution for you may be as simple as finding the one with a branch closest to your home. But savvy consumers should be on the hunt for more — a checking account that doesn’t gouge you with fees and a savings account that pays more than a pittance.

Bankrate.com partnered with MONEY to find banks and credit unions that offer the ideal combination of accounts — a free checking account (or one as cheap as possible) and a savings account that pays a high interest rate (or at least keeps the monthly fees at bay).

There aren’t many banks and credit unions that do both types of accounts well. Those that do earn their title as one of the best banks in America. Here are our picks.

Best online bank

Bankrate's 2017 Best Online Bank Award San Diego-based Bank of Internet USA clinched the top spot among online banks with a one-two punch of yield and cash-back rewards. Founded in 1999, this online-only bank is one of the pioneers of branchless banking. It has long been regarded as a deposit rates leader.

Customers who open a Rewards Checking account can earn as much as 1.25 percent APY on their money if they have direct deposits totalling more than $1,000 a month and use their debit card on at least 15 transactions of more than $3 a month. Customers also can earn cash-back offers by logging onto the bank’s website, browsing offers and clicking to activate them.

The bank’s Smart Savings Account pays 1.05 percent APY. That’s more than four times the national average savings account rate, according to Bankrate’s most recent national survey of banks and thrifts.

You won’t pay a monthly service fee on either account, so customers don’t have to worry about maintaining a certain balance or opting in to special features to dodge a fee.

One potential danger customers of internet banks face is ATM fees. Few or no branches may mean a small ATM network. Bank of Internet shines, though, offering unlimited domestic ATM surcharge refunds.

Both accounts are available to savers nationwide.

See our other picks for best online banks.

Best credit union

Bankrate's 2017 Best Credit Union Award Alliant Credit Union achieved a near perfect score in our rankings for its solid products and accessibility. This Chicago-based credit union boasts more than 335,000 members nationwide. While it operates branches in four states and Washington, D.C., Alliant offers a strong online banking experience for its members elsewhere in the U.S.

Alliant’s High-Rate Checking carries a 0.65 percent APY and has no minimum balance requirements or monthly service fee. To earn interest, you must accept electronic rather than paper monthly statements and have at least one monthly electronic deposit made to your account. Acceptable electronic deposits include direct, payroll, ATM or mobile deposits or a transfer from another financial institution.

Its members have access to more than 80,000 surcharge-free ATMs nationwide, and Alliant refunds up to $20 of out-of-network ATM fees monthly.

Alliant Credit Union’s High-Rate Savings account pays 1.16 percent APY. The account requires a $5 initial deposit (which Alliant will pay for you), and there is no monthly service fee.

Bankrate also gave Alliant high marks for its membership requirements. Unlike most credit unions, Alliant doesn’t restrict membership based on where you live or the company you work for. Anyone can join this credit union by donating at least $10 to the Foster Care to Success organization, which helps foster teens who are aging out of the foster system.

See our other picks for best credit unions.

Best big bank

Bankrate's 2017 Best Big Bank Award Capital One’s ability to straddle two worlds played a hand in its ascension to the top spot on our list of the best big banks in America.

It has a national reach as an online bank, but Capital One still very much a brick-and-mortar shop in places like New York, Louisiana and Texas. Although its branch network is smaller than some other big banks on our list, Capital One still ranks among the 10 largest banks in the U.S. by assets.

The bank’s 360 Checking Account pays 0.20 percent APY — decidedly lower than our top credit union or online bank. But interest-bearing checking with low or no fees is practically unheard of for big banks. Not only does Capital One pay, it charges no monthly service fee.

Keep in mind the potential for ATM fees, though. Capital One says it offers 39,000 free ATMs nationwide (including bank-owned ATMs and those part of the Allpoint network). But if you use an out-of-network ATM, Capital One will charge you $2 — and you may incur an additional fee from the ATM operator.

Capital One’s 360 Savings Account pays 0.75 percent APY, which is eye-popping, considering most big banks pay a smidge above nothing. That account also has no monthly fee.

See our other picks for best big banks.

Best regional bank

Bankrate's 2017 Best Regional Bank Award Banner Bank in Walla Walla, Washington, scored high points for breaking down the barriers to getting cash. We rank it the best regional bank in the U.S.

Banner Bank operates nearly 200 branches in five western states: California, Idaho, Oregon, Utah and Washington.

Its Connected Checking account gives customers unlimited free out-of-network U.S. ATM use, and Banner will refund charges imposed by other ATM operators. The checking account doesn’t have a monthly service fee. It pays no interest, either.

Of the 62 regional banks Bankrate surveyed, just four offered a savings rate above the national average. Banner is not one of them.

Its Connected Savings account pays a 0.05 percent interest rate on balances above $25. We like this account because its $3 monthly service fee can be avoided in a variety of ways, including maintaining a minimum daily balance of $100 or with an automatic transfer of at least $25 from a Banner checking account.

This is a decent place to park your emergency savings, but this bank account should not be considered as a place to grow your nest egg.

See our other picks for best regional banks.

How we chose the winners

Bankrate gathered checking and savings account data from 75 brick-and-mortar banks, 50 credit unions and 15 online banks. In doing so, we examined more than 800 accounts and 18,000 data points, looking at the fees each institution charges and the deposit rates it offers. We also looked at factors like the number of branches a bank or credit union has and the number of states in which it operates.

For the survey of the best banks in America, Bankrate chose one checking account and one savings account from each institution. When an institution offered more than one checking account, we chose the one that offered free checking or the fewest barriers to avoid a monthly fee. In cases where an institution offered multiple free checking accounts, we chose the one that paid the highest APY. If it offered more than one savings account, we chose the one that offered the highest APY at the lowest monthly fee.

We assigned a number grade to each institution on a 100-point scale, looking at criteria including monthly service fees, interest rates, ATM and branch access (for brick-and-mortar institutions), ATM fees, mobile app ratings and minimum deposit and minimum balance requirements.

For online banks, we gave the most weight to the checking account monthly service fee and how easy it is to avoid it, the savings account rate and user ratings of its mobile app.

For brick-and-mortar institutions, we gave the most weight to branch availability, the checking account monthly service fee, ATM fees and the savings account rate.

See MONEY’s picks for the best bank in every state.

Editor’s note: Special thank you to Adam Bean, Daniel Cocozello and Brett Wilkinson from Bankrate for gathering checking and savings account data from 75 brick-and-mortar banks, 50 credit unions and 15 online banks, allowing us to examine more than 800 accounts and 18,000 data points for this ranking.