Hi I’m planning to have a tattoo and I would like to have a translation in Latin of “God and Family”. Which one is appropriate, "deo et familia" or "deo familiaque"?
It would really depend on several factors. Like the comment above stated, it would depend mainly on the case used for the slogan. This would be determined by how that phrase would apply to you and be used in a sentence reflecting that. Are you saying that you belong to God and family, that you are giving yourself to God and family, or that you draw your essence from or by God and family?
Also while both of those "and"s work, usually in slogans we see A et B.
Given those factors your options are as follows:
of God and Family: Dei et Familiae
to/for God and family (especially if you are dedicating yourself to them): Deo et Familiae
by/from God and Family: Deo et Familia (remembering to put macrons over the final "o" and "a").
Syntax and case matter. Remember that slogans are usually derived from a complete thought and their role in that thought is what determines what case is used.
P.S. As is noted in the comment below if what you wanted to say was "[the most important things to me in life are] God and family," that would be Deus et familia. Still, the other uses might make more sense especially since tattoos are usually an act of dedication, but it is really up to you.