Try the NE5532 or TL072.
Note that there's no point in specifying so many significant figures for the resistors, because the capacitors will have 1% tolerance, at best, 10% being more typical. If you use 1% tolerance capacitors, then use the nearest standard E96 resistor value of 3k4.
The circuit should work. The simplest way to limit the output, without horrible clipping is to use diodes to bypass a resistor, once the output voltage gets too high. In this case
AV = 1+(R4+R5)/R3
When either D1 or D2 start conducting R5 is bypassed lowering the gain towards 1+R4/R3.
Increasing the voltage across the diodes reduces the output, but will increase the distortion. Replacing them with Schottky diodes, such as the BAT54,, will lower the output voltage.
Taking the output from the other side of R5 will give a cleaner sinewave, but it's a high impedance node, so will need a unity gain buffer, but if you're using a dual op-amp, it's free.