Thanks for popping into the forum!
When it comes to getting into an MBA, the only thing you need for certain is a relevant bachelor's degree (which you will have). The rest will vary by university, but may include the following:
- Academic merit (depending on the prestige of the university, you will need higher marks)
- Letters of recommendation (academic or professional)
- Full-time professional work experience, preferably in a managerial position (some programs do not require this and if you have experience within the family business, that may qualify)
- Qualifying GMAT or GRE scores (Most B-schools ask for the GMAT, but many now accept the GRE)
In terms of which specialization to choose, that may depend on the nature of your family business. Without context, a general MBA in Management could be of great help. You can browse common specializations here. If you don't mind, what sort of business does your family run?
Once you have narrowed down your interests and choice of specialization, you should choose a university based on the strength of their programs in that area - in addition to other factors that may be important to you, such as ranking, diversity, class size, etc.
This has been a bit general, but in short, the right program is the one that best fits your requirements, so you should start there.