How do I approximate number of calculations/operations/memory/hardware is required for a 2^18 point FFT on chip?
Well, an \$N\$-point FFT will require \$\log_2N\$ stages, and each stage will have roughly \$N\$ multiplications and additions (although many of those will turn out to be trivial once you see what the twiddle factors are).

If you want to pipeline the computation then add \$N\$ flip-flops for every pipeline stage.

The actual complexity in gates or LUTS for a multiply/adder will depend a great deal on the nature of your input data type and your accuracy requirements. On the other hand, limits on the silicon resources and power will limit how much computation you can really do.