I am about to Travel to Germany on Business visa. I want my family to accompany me, and we wish to tour around for a week or so. The total head count is three people. My intent is to go there and possibly apply for a work permit from Germany.
Should I apply for Business+Tourist visas (for family) together OR should I first get the Business VISA, then post getting it apply for the Tourist visa's? Is there are any preference from any of your experience, or does it not matter?
It would be up to you to decide whether to apply for a visa for yourself and, separately, for your wife and child, or to apply at the same time.
If you have a business reason to visit Germany and want your wife and child to accompany you, do as you say: apply for a business visa, and tourists visas for your family members.
Done separately or together doesn't matter: you will apply through the same consulate, and the information on your visas entered into the Visa Information System (VIS) which allows Schengen States to exchange visa data. It processes data and decisions relating to applications for short-stay visas to visit, or to transit through, the Schengen Area.
If, as you comment, your intent is to find work, then, rather than risk a refusal of one, or all, of your visa applications, a safer plan might be to go the route that allows you to work and live there.
Germany has online tools and information which streamline and facilitate this process, and Make It In Germany* has everything you need, be it as an individual or as a business.
*Under the auspices of the Federal Ministry for Economic Affairs and Energy, the Federal Ministry of Labour and Social Affairs, Bundesagentur für Arbeit (the Federal Employment Agency, the largest provider of labour market services in Germany).
