I would use MKP, which is made of polypropylen foil. A polyester type is not so good, because its capacitance is freqency dependent.

If you use TL081 instead of TL051, then you must at least select a device which does not show an offset voltage of more than 2mV! So, take a handful and choose a chip providing this very low offset voltage.

Again, I would heavily recommend only to use TL051 instead of TL081. TL081 is not stable enough!!!

C1 must sit close to OPamp, otherwise it will not show much benefit.
Keep in mind, that a circuit which is such precise, needs a solid ground plane. If it's not possible to provide such, manage at least a star point ground routing. Have a look for instance at the grounds of input and output connectors. If interference is hitting input cable, then it will run via the narrow ground trace to ground pin of output connector. The voltage drop it causes here is directly added to the potential at non-inverting input of OPamp!! This is not allowed! Route the ground at the connectors in such a way, that no interference is added to OPamp signals.

Copper traces at inverting input of OPamp should be as short as ever possible. Everything connected to inverting input of OPamp need special care. The signal routing here should be embedded into a ground plane. In more sophisticated circuits, this area is even 'guarded', by totally surrounding it by a copper trace which is connected to potential at non-inverting input.

Take care, that this circuit is well shielded. If the circuit is hit by hum or HF interference you will never get a stable reading.
Keep in mind, that no HF filter was added at input. The reason was, that if you increase integration resistance from 10kOhm to 100kOhm or so, then even only 100pF capacitance to ground would cause an error of about 5% at 5kHz, which is a relevant frequency in your thyristor chopped application. So, if you finally use such a high input resistance, a HF filter would be difficult to implement. Then you would need a shielded Rogowski coil!
Another remedy is to use a Rogowski coil which will not need very high input resistance, less than 10kOhm. Then an additional HF-filter can be implemented: Put a 1...2.2kOhm resistor followed by 100pF capacitance to ground at the input of circuit.
But don't expect too much from this filter. It would be better in any case to use a shielded Rogowski coil, remember the picking-up of swicthing noise from wire, which carries the current to be measured.

Take care, that the whole application is surrounded by a complete Faraday cage, which is only once connected to ground, where the cable enters the enclosure.

Kai