What Approach To Choose Time & Materials (Per Hour) + Agile or Fixed Price + Waterfall?

If the business or end product requirements may change:
Time & Materials Model (Per Hour) + Agile Approach + Agile Requirements Management
If you have a small project, stable requirements and want to get the best fixed price offer:
Fixed Price Model + Software Requirements Specification + Waterfall Project Management
In either case we generally propose to start our business relationship with a risk-free Pilot Project.