Can I bundle several requests into one proposal, or is it best to separate them?

We need funding for building and equipping an orphanage, and we also need start-up funding for salaries, etc. Would it be better to approach these funding needs in stages, with Stage One being the building, Stage Two being the equipment, and Stage Three being programming?

Yes. Generally, it's best not to lump capital projects (building projects) and operations into the same funding request. Submit requests for capital projects to grantmakers who have a history of providing that specific variety of support. And submit grant requests for program funding to grantmakers with a demonstrated interest and funding history that's appropriate for that request.

But, start by laying out the big plan, and always keep that in mind. Stages or Phases are logical ways to break down the big plan.