The reason that some people do a climb pass first, followed by conventional, is this.
At high chip loads like this, the cutting forces are pretty high, and with a conventional cut, will tend to pull the tool into the part, resulting in a slightly undersized cut.
This can also happen when onion skinning. The first pass will pull the tool into the material, but the final pass will be more accurate, and leave a small lip on the bottom of the part.
By doing a climb cut first, the tool is actually pushed away from the part, which leaves a small amount of material for the final, conventional cut.
But the climb cut won't cut as clean, especially as the tool starts to wear, so it may leave chips that won't be removed on the final pass.