Any suggestion for the best pipeline for INDEL (Insert/Deletion) calling based on illumina NGS DNA sequencing?
GATK is your best bet for human data, however for larger structural changes you may need to look further afield.
Definitely would go for GATK first, specially for the recalibration and pre-processing of aligned reads that is done by GATK and then its downstream handles to associated INDELS, if it does not yield something very specific or have large number of INDELS, then the processed GATK aligned files can be used to other downstream INDEL identifiers like FreeBayes, DINDEL, PINDEL, SomaticIndelDetector. I am only highlighting those I have experience with. There are plethora of tools but everything boils down to the fact which tool gives you regions of INDELS that upon annotation makes sense of your phenotype or hypothesis.
FreeBayes, DINDEL, PINDEL, SomaticIndelDetector