One thing about plywood to consider is that it HAS A GRAIN. This means if the span between brackets is large enough and the weight the shelf will hold is heavy enough it will sag. You can prevent this to a large degree by fastening a 1x2" strip of solid pine on edge under the front of the plywood. Apply this on the full length of the shelf. 3/4 " plywood might often be enough, but 1" is better if you have to deal with very heavy loading.

Another cheap alternative is 3/4" OSB. The advantage is that it HAS NO GRAIN he strands support each other in every direction. The same thickness of wood will support more without sagging because of this. Applying a solid 1x2 under the front edge will do even MORE to stiffen it and prevent sagging. OSB can be sealed and clear finished, too or painted if you don't like the look. This is what I used on my own garage shelving with a clear varathane finish.

Well, the thicker it is, obviously, the sturdier it will be, but with that much weight on a shelf I think you're going to have problems. The plywood is going to end up bowing under the weight unless you spend the extra money for much thicker plywood and even then I wouldn't be too sure. It would be cheaper and better to install more supports for the shelving, every other stud or even every one.

I would probably consider using two 1 x 10's or 1 x 12's of pine.

I'm building a bunch of shelving in our garage using stud-mounted metal tracks/brackets with plywood shelves. I'd like to get 4-foot spans (with 20-24" depths), but I want the shelves to be sturdy enough to carry 200-300lb loads (evenly distributed). I would like the shelving to be somewhat smooth, but these are garage shelves - not going in the study.

Will 3/4 plywood do the trick? I know very little about wood. What, specifically, should I look for at the hardware store that will provide the best value and meet my needs?

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