I'm putting Burnham as my second preference with no others. I think he could actually be a very useful part of Corbyn's team, and in a new political paradigm may finally have the courage of his (rather well-hidden) convictions.
It's important that the party stay unified after the election. If Corbyn wins he would ideally get the support of all of the other candidates as part of that unification process. It's unlikely that Kendall and Cooper would support him or join his shadow cabinet. Burnham has indicated that he would join and will support Corbyn. To maximise the unifying effect of that it would be best if Burnham came second in terms of number of votes cast. It can then be said that the two candidates that got the most votes are working together etc.