How to build attic space in garage
If you're placing 2x4s between the trusses, it's fairly easy to face nail them (at a slight angle where necessary), rather than toenailing, which often results in splits and less penetration. Either is fine if done carefully.

You may be better off using 2x10 joists for your floor, and notching them over the trusses to flush the bottoms for the ceiling drywall, or maybe hang them between with joist hangers. 

Step one is to verify that your truss system is designed to handle the additional load of storage. Do you have the original spec sheets? Be very careful about loading the truss system with more than a few hundred extra pounds on the bottom chords,and be sure to distribute the load. Even if the trusses as a whole can carry the load, the bottom chords and their attachments may not be up to the task. 

Then, you'll need floor joists at no more than 24" centers, depending on the floor sheathing you intend to use. These probably will be toenailed. They'll likely run directly above your furring strips. 

Finally, you'll need to work out how to insulate with framing running two directions. I envision R-19 laid parallel to the trusses, and maybe R-19 or better running perpendicular, between the floor joists.