While I may be stating the obvious, hospitals and health systems are complex creatures that frequently drive local economies, culture and population health status (among other things). Accordingly, when considering a potential change of control transaction, it is critical that you examine what drives your organization and what [in the community] your organization drives. In particular, the latter is frequently overlooked in these circumstances.
What Drives Your Organization (Your Mission)
So, how do you begin to identify your organization's priorities? I recommend starting with the low hanging fruit—the hospital's mission. It is critical in the early stages of a potential transaction to consider your organization's mission, how that mission relates to your current operations and if that 
mission is capable of evolving. For instance, if your hospital's focus for the last 50 years has related to teaching and research, then partnering with an organization that will continue to enhance and invest in these pursuits may be a key priority. Likewise, if charity care and serving the indigent population has been the hospital's mission historically, you will want to ensure charity care is high on your list and considered when your board evaluates a potential transaction partner. These are the points on which you will be less likely to compromise as the deal progresses.
What Your Organization Drives
Next, I suggest identifying the tangential (although, no less important) role(s) your hospital may have in its community. Compared to the above analysis, this step may be less crucial to identifying the best transaction partner. However, these considerations are important to ensuring the overall success of a deal. For example, hospitals are frequently among the largest employers in a region and may have some of the largest contracts with other service providers in their communities. Hospitals often attract other independent providers (physicians, medical suppliers, other providers) who serve an important role (and tax base) in the local economy. If you partner with the hospital next door, is the transaction more likely to result in a consolidation of resources that affects your employees or the community in ways you did not anticipate? It may be that you have a service contract with a local provider that a potential partner finds unnecessary / undesirable—would terminating your relationship with that local business lead to its demise? Of course, you may see some overlap between the hospital's mission and the priorities you identify as part of this analysis (e.g., undeniably, charity care also plays an important role in the community). However, these are the sorts of considerations that are easily forgotten in the haste to vet a potential transaction partner. Despite this, these considerations may be some of the most important to the long term success / acceptance of the hospital post-transaction.
The Mack Truck That Decides For You
Further complicating matters are those items beyond your control that will inevitably influence how or what you prioritize. For instance, perhaps the requisite approval of your state attorney general requires your hospital place the continuation of charity care at the top of its list of priorities. Or perhaps an unexpected capital expenditure creates a need to select the financially strongest partner. Consider also, is your medical staff completely resistant to a change in certain policies? It is important to identify these types of factors and anticipate early on how they may affect how or what you prioritize.
Knowing what you need and what you want is the first step towards getting both. Only after you prioritize your organization's needs and wants for the future can you effectively work with counsel to develop deal terms to achieve those ends. By first identifying and prioritizing your organization's objectives, you best position the hospital to ensure its goals are achieved, whether through careful transaction structuring or advantageous deal terms.