At what processing step should library strandedness type be taken into account?
I usually take into account library strandness during the mapping to the reference step (but I never worked with bigwig files myself). 

Assuming RNA-seq data from Illumina, you can use Hisat2 for alignment to the reference genome, and you have the option --rna-strandness to specify the strand-specificity information (default unstranded). This is particularly important when you wish to have XS strand attribute in your bam file for easier compatibility with downstream software (especially important in my experience if you are planning to use some utility from Cufflinks for your step 3).