Evaluating Software Suitability

The method I've always used for determining how well a software tool fits as a solution essentially boils down to this:

1. Document process
2. Build Use Cases
3. Evaluate software fit with use cases. Double check fit using process documentation.
4. Evaluate software's fringe benefits (nice features that don't solve primary use cases/problems)
5. Evaluate cost, ROI, vendor viability, etc
6. Consider how software will impact future systems and designs.

I know there is probably better terminology for these steps. This is basically my home-brewed method and it's based on the purchasing processes used in the various organizations I've worked in over time. 

I'm sure there's a framework out there for this sort of thing but I haven't really been looking for one. I just want a good, simple process.

How do you evaluate how a software tool will fit your organization? See any flaws in my method (I'm sure there are some)?