Can I suspend garage storage from the ceiling alone?
Can I suspend both sides to the ceiling? 
Yes, if:


Your ceiling is capable of supporting the weight. You're typically dealing with 2x4 truss chords, but I have no idea what your situation is. I'd consider laying a sturdy crossbar across several ceiling joists to distribute weight, and fasten your uprights to that. 
You fasten properly. Don't rely on bolt pullout strength unless you size them adequately. If using the 1/4" lags you mentioned, they should be installed horizontally, tying your uprights to the crossbar or ceiling joists. This places the load in shear rather than tension. If you must install screws vertically, use 7/16" or 1/2" lags, piloted properly, and with adequate penetration.
You don't need the stability that wall attachment provides. If you're not tossing heavy objects up there regularly, where movement is a concern, this shouldn't be a problem. 


What fasteners should I use?
Again, that depends on your design. I used nothing but 2-1/2" gold construction screws for my full-length racks, but I only use them in shear and I use multiples where needed. 1/4" lags are a good idea.