On 3/4" MDF I use 1-1/4" brads (18 gauge). Never had any problems with splitting. You might have problems if you try to use 15 or 16 gauge finish nails though.
The brads just hold the work together while the glue sets, that is really their only purpose. I use the lightweight vinyl "spackle" to fill the tiny holes where the brads penetrated the wood. It's cheap, paintable, sands reasonably well, dries reasonably fast, and doesn't shrink when it dries.