You will need to apply at the embassy/consulate of the country which is your primary destination.
From the EU website:
You must lodge the application for a Schengen visa at the Consulate of the country that you intend to visit, or – if you intend to visit more than one Schengen State, the Consulate of the country where you will spend the longest period.
Requirements to apply
From this document:
Who can apply for a Schengen visa in Saudi Arabia?
Saudi Arabian nationals and third-country nationals who are legally resident in the Kingdom can apply in Saudi Arabia.
What is the fee for a Schengen visa?
The visa for adults costs 60 Euros (or the equivalent in Saudi Riyals). The visa for children under six years is free. Children from the age of six years and below the age of 12 years pay 35 Euros. For exemptions check the website of the Member State through the links below. If applications are processed through a visa application centre, an additional service fee applies.
More information on Schengen visas can be viewed in that document.
And yes, to make it easier you can apply for a family Schengen visa.