Non-inverting amplifier ; Single supply ; Bipolar input
Good start, just one more thing to add...
R1 cannot be DC-grounded. It must be AC-grounded with a capacitor. You would choose the capacitor value so that its reactance is equal to (or less than) R1 at the lowest frequency that's important to you. For example, if R1 is 1000 ohms, and you are amplifying audio where 20 Hz is the lowest audio frequency, C1 (below) is about 10uF.

With such a low DC supply voltage, a rail-to-rail opamp is a good choice...many common opamps cannot provide enough output signal swing with a +5V supply.







simulate this circuit &ndash; Schematic created using CircuitLab