It may be helpful to think of outsourcing options at two levels: those activities that are strategically important in support of your customer value proposition and those that are more routine requirements for your business. It seems you're talking more about strategically important work, and for that it's helpful to have a partnering type of relationship - the outsourced provider becomes a virtual extension of your company. If it makes sense to consider the relationship this way, your attention to cultural fit is spot on. The total cost of services provided by your outsourced partner will be affected by many intangibles, e.g. trust, so attention to cultural fit will also support the economics of your choice.
As far as further activities go, the principal focus needs to be on communication/collaboration. While technology can create a fabulous infrastructure for collaboration these days, it will be extremely helpful to establish key contacts on both sides of the relationship. The value of key contacts comes from relationships: key contacts feel the need to be available and responsive in a way that faceless corporate entities often do not. Therefore, one activity to address early is helping those key contacts to meet in person and get to know one another.