My very strong recommendation is to test with the Wilcox project (which of course includes all the surname variations) through Family Tree DNA.
Test a minimum of 37 markers of yDNA, which should in most cases locate your male within a family group. A total of 67 markers -may- help determine branches of that family.
This is the most well-established form of testing, with the largest database, and is the best choice for tracing a direct paternal line.
The "most comprehensive" test is Family Finder which may produce results in -any- of your father's lineages. (Or your own, for that matter.) It's new and spendy, the database is still small, and it will only be useful to those who already have a well-documented pedigree, but it holds great promise for the long haul.