Both are seperate you can't choose which one you need to pay.
Both are separate and you can recover the GST amount from customer so how will it be your cost.
By the way I would suggest you to take GST registration when your receipts cross over 20 lakh. Your export after GST would not cost you anything as export under LUT is zero rated.
But if you take registration before crossing the limit you will have to pay GST on services provided within India.
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