Family Tree DNA
Family Tree DNA (FTDNA) is the oldest and largest Y-DNA and mtDNA testing company for personal/genealogical usage. They offer both Short Tandem Repeat (STR) testing (in bundles 37 Y-STRs and 111 Y-STRs) as well as Single Nucleotide Polymorphisms (SNPs) through their Big Y-700 test. Prices for these products are available at their website and they have sales from time to time.
The size of a dataset is important as the larger the dataset, the more refinement can be made in placing the family into what is called their "Haplogroup". By and large their Y-DNA haplotree is the de facto standard in the genealogy field. Their mtDNA haplotree currently only is broken down by the PhyloTree standard (Build 17, which dates back to Feb 2016 with no plans on updating the standard). FTDNA has stated they will be updating their haplotree as part of their "The Million Mito Project.
The GSMD sponsors the Mayflower DNA Project led by Robert "Mike" Terry (Kenneth Whittemore assisting on the Y-DNA side) with Susan Abanor working on the mtDNA side. There are a number of surname projects associated with Mayflower passengers as well as the sons in-law.