Shift left followed by round for performing: y=x+cz in hardware
If you shift z right first you will immediately discard the lower bits of z. That information is gone forever.

If you first shift x left and keep all of its bits, then add z, you will have preserved as much information as you can. Rounding back to 8 bits at this point will give you the most accurate answer.

In general, when using integer arithmetic you want to defer division as long as you can. Do all of the multiplications and addition first, then have one final step where you divide with rounding.