I would recommend you choose 2 or 3 colours and then mix and match them between you. This works really well in a studio portrait.
Using different shades of the same colour also works really well. If you are a family of all girls you could use different shades of pinks and creams and then put dad in denim and grey or grey and white.
For a family of boys, you can use blues, greys, denim and whites. This also works for girls, you can put them in a dress to add a more feminine take on the blue for example.
Personally I also love images when you are all wearing white or white and denim. White, denim and grey also work well.
Avoid busy patterns, stripes, and mixing very bright colours.
Simply, natural, pastel colours are perfect.
I always not recommended wearing clothes with shiny reflective items like beads or sequin.