Alveolus,
If time was not an issue, I would do all four. Each provides a wonderful outing.
If you are going to do just one of the four, then carefully study the maps and online trip reports/photos and see if one is particularly appealing to you.
Also, there are other interesting approaches, but these typically leave the trail at some point and then head for the Summit of Mt Whitney.
Let us know what you ultimately do and send us a report. Many others will be doing these hikes this season and would like to hear about the conditions.
Jim