Non-inverting op-amp with DC offset
Easiest method:







simulate this circuit &ndash; Schematic created using CircuitLab

Component values are left for you to calculate.  

Note that the TL081 is NOT an appropriate op-amp, given your desire for a rail-to-rail output swing.

R1 &amp; R2 set the op-amp bias point. 

R1, R2, C2 forms a low-pass filter that reduces noise from the power supply 

R5 sets the input impedance 

R5 &amp; C3 set the input hi=pass filter time constant

R3 &amp; R4 set the gain.

R3 &amp; C1 set the gain-set section hi-pass filter time constant.

Note that if you are not concerned about noise from the power supply line getting into your amplified signal, you can eliminate C2 &amp; R5.  In that case, R1 &amp; R2 set the input impedance and R1, R2, C3 set the input hi-pass filter time constant.