Why would it matter how much you invest? You will earn a higher interest rate without all the fees and minimum balances most all banks have.
Currently ING checking is offering:
$0-$49,999.99 1.74 %
$50,000.00-$99,999.99 3.25 %
$100,000.00 or more 3.45 %
Savings:
3%
Both are better then most any standard checking or savings account, again, with no minimum balance or fees. You can even have a ATM/debit card just like any other bank, with many ATMs. There are other online banks that may offer slightly better rates but rates will change all the time. It would be a waste of time and trouble to chase rates for a few extra points, in my option. Only down fall I don't care for is, you have to have direct deposit or mail in deposits. But, to avoid that, I have a brick and mortar bank I make deposits to, then just transfer funds between accounts.
These types of accounts are perfect for emergency funds or other things you might need to stay liquid for but want to collect a few extra bucks. Every penny counts.