The buy versus rent choice is really another way of saying: cloud or on-premise systems. A non-profit can get huge discounts off the commercial rate on software or services either way. The capital expenditure versus expensing doesn’t really matter to a non-profit.
Five years ago, a non-profit would go to techsoup.org and get most of what they needed – servers, desktops, and software. You can still do that and, in some instances, it makes good sense. But you can now get your phone system, email system, file server, back-up, work flow, accounting, and CRM all over the internet. Not having the server and a PBX in the closet avoids a big sunk cost and major maintenance costs. Now that desktops (laptops) are down to $400 each, they aren’t as major an expenditure anymore. Desktops (client boxes) are also less important if users are spending most of their time in a browser. The maintenance can be monitored remotely through cloud services as well. You can even rent Windows and MS Office.
If you are starting from scratch or starting over, your major cloud/rental options are Google Apps (maybe even Google laptops) or Office 365. They are in heavy competition and, therefore, working hard to beat each other out. Both offer non-profit pricing (that is not very well-publicized). I’m doing projects in both right now. Consider that users are also going to want to bring in their own iPads, smartphones and laptops and hope they will function with your systems. Whether you go with renting, buying or a combination of the two, someone should spend a good number of hours analyzing and implementing the options.