MDF Splitting

It sounds more like the way you're putting the screws in.  MDF is going to split if you don't pre-drill (I found this out the hard way, long ago).

If you're screws are #10's, then you would use either 9/64 or 5/32 for a drill bit (or 25-27 if your bits are in wire guage), in my opinion.  It's pretty easy to size them up, all you need to do is put the bit next to the screw and pick the one you want.  Just remember to drill the entire depth that the screw is going in, no more.  Do this by taping the length that you want on the bit.  When you reach the tape while drilling, you've gone far enough.