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Reconstructing Phylogenetic Tree / missing data


Hey peeps !

im very new to phylogenetics and currently trying to read myself a bit into the thematics of tree construction and getting started with all the different tools/software.

i would like to reconstruct a tree of 138 cyanobacterial strains defined by 16S , 16S-ITS , rpoc1 , RnaseP , rbclx , PC-IGS , PSA-IGS. The authors originally constructed the tree using maximum likelihood and the F84 model

I would like to implement another 4 strains where i got all loci sequences except the 16S-ITS. Now im not sure how to deal with missing data , should i construct a tree with all loci where i got missing sequences for only 4 strains , or should i use just the loci where i got total coverage ? is there a way to find the “best” method and will the choice of algorithm or substition model be influenced by this ?