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Want to open Money Market or Savings, advice please.?

I’m wanting to change my traditional checking/savings account to Internet based higher yield APY account. I was looking at bankrate.com and I noticed the higher yield accounts are not known banks. Are they safe to deposit money to? Should I go with known bank with lower APY? I’m looking to find a account with checking acct. link ability to transfer money to/from, and wanting to deposit our monthly income there and be able withdraw when we need it. What is the good going rate for MMA or savings account? Which company is good to open with? There are so many out there I don’t know which one is good or risky. Thank you.

I just opened an on-line savings account with FNBO this morning. FNBO stands for the First National Bank of Omaha.
I had an account with them before and the ease of maneuvering money is simple. Right now, the APR is 3.85%.
FNBO is on bankrate.com and their accounts are FDIC insured. You should not have any problems. One thing to remember is this: Everytime the Federal Reserve cuts the rate, then the rates at banks will be lower. Guess what? The Federal Reserve is meeting on March 18th and it is expected that the rate will drop .75 of a point. Great for borrowers, bad for investors. I want to see the rates go up and stay there.