If the nonprofit is new, the most important question to ask is: "Do we need to exist as a separate nonprofit?"
There are more than 1.2 million nonprofits around the country. There is tremendous duplication of services. I would strongly advise you to pursue a strategy such as:
1. Partner with a strong and stable 501(c)(3) to become a program underneath them; they can handle the back office stuff, and you focus on delivering your service and raising money. Your board can then be an advisory board/committee of their governing board, which is much easier to setup and easier to recruit for.
2. Setting up the charity as a designated fund at a community foundation. This is similar to the above scenario, but you likely have much more control over back office stuff.
However, if you are dead set on opening your own 501c3, there are a few things to look for in board members:
1. In the beginning, most boards are "working boards" (i.e. they do many of the duties of staff members). Therefore, targeting prominent society figures is likely not a good fit. You need people willing to roll up their sleeves and do the work. And therefore you need a variety of talents: someone to help with financials, someone to help with setting up the internal tracking systems for donors/clients/etc, someone to help with policies and procedures, and someone (or several people!) to help with fundraising.
2. They need to have a very clear understanding of their role. You should have job descriptions that clearly outline expectations, including how much they need to donate and serve (and they MUST be willing to do both .... donors give cash, volunteers give time and board members give both).
3. They need to be willing to help raise money. This does not necessarily mean calling friends for cash, but they need to be willing to fill a table at your launch event and invite people to go on tours/meetings with the ED. Above all, they need to NEVER apologize for the org's need for money. Inviting people to invest in a life-changing mission is a privilege, and they need to understand that.