DNA tests recommendations

My name is Delia Dominguez Duran. I am a member of Nuestros Ranchos as l have attempted to discover my ancestral roots. My question to you is whether you can recommend an organization and or testing site or type of test I can employ to determine the racial group or groups
that might give me insight to my genetic roots.
I am also a member of Ancestry.com , and they do offer a site but am not familiar with DNA testing and if one site or type of test might be better than another.
My maternal grandparents were born in the Mexican states of Jalisco(Mora / Rodriguez surname) and Aguascalientes (Rodriguez/ Reyes surname) Paternal grandparents Arizona (Dominguez / Hernandez surname) paternal great gandmother possibly Chihuahua via Zacatecas (Hernandez / Carbajal surname) .
Can you recommend a type of test or organization that will help establish my genetic roots .
Respectfully,
Delia Dominguez Duran
rsduran@aol.com