Non-inverting op-amp saturating incorrectly
Figure 1 doesn't work because the op amp input is driven out of spec.  Some op amps reverse polarity in this situation, others (like the LT1014) don't.  But inearity is lost, so this regime must be avoided if the wave shape is to survive.
Figure 2 works just fine, but I guess you don't want to use a split supply.
Figure 3 has the input signal biased to VCC/2, which is good, but the amplifier is referenced to 0V (ground end of R4).  This shifts the mean value above VCC/2 and reduces dynamic range.
Figures 4 and 5 do all of these things right but now the output biasing is not needed (in fact, it just draws unnecessary current from the Amp).  A fitting value for the amplification is obtained by choosing middle ground between R2 being 1k and 60k.  And the impedance of the caps at your frequency should be a good deal lower than that of the biasing resistors, basically
$ 1 / (2 \pi f C) &lt; 5k $.
The signal clips asymmetrically in Figure 5 because the LM324 output swings to ground, but not all the way to VCC.