A 28" long shelf made of 3/4" thick MDF will eventually sag up to an inch. You can minimize that sag by adding a piece of wood about 2" wide to the front of the shelf---making a lip which adds strength.

Making 1/4" deep dado's and using glue/wood screws with coarse threads(1/4" by 1&1/2" long) will be better. You must predrill and do not use a power driver to fully seat the screws---too easy to strip out the threads in the holes.

If you can't make the dado's, glue/screw 2" strips of wood on which to install the shelves.

Reason is that even glue/screws used on butt joinery will not hold MDF shelving over time.

The HD near me stock MD at around the price you mentioned, so that's probably what it is.

Regarding your plan, I'm with handymac, it will probably sag if installed as you describe. And drywall screws into the MDF doesn't sound strong enough even to hold it up in the long term.

MDF has some wonderful qualities, but it is weak, and very heavy. For those reasons I usually employ strategies along the lines of what handymac described. For shelves, in fact, I often use 1/2" MDF with a glued-on lip and perhaps glued on undershelf support strips of 1/4" or 3/8" dimensional material. This give you the strength of real wood with the smoothness, paintability, dimensional stability and economy of the MDF. (Finding the appropriate strips of wood could be problematic if you don't have a table saw.)

If you don't have a table saw, probably the best strategy is to create cleats made out of 1x2 material to support the MDF, with a 1x2x28" support connected to the front of the cleats to provide longitudinal support. Wouldn't look as good as the dado approach, but it would hold up well.

Cabinet light rails make excellent stiffeners when applied to the front edge of the MDF. They are pre-notched 3/4" to fit over cabinet stock and will slip over the front edge of the shelf about 3/8".

Michael