raw: output values are probabilities (0 - 1), the sum of all cells used during training is 1. Therefore, most of your values will likely be very small
logistic: also probabilities (0-1), but scaled up in a non-linear way for easier interpretation. If the probability of presence is ~ 0.5, log output can be interpreted as the probability of occurrence at that location.
sum: value of a grid cell is the sum of the probabilities of all cell with no higher probability than the focal cell, times 100. Best conditions at 100, unsuitable near 0.
Logistic is probably your best option, but some evaluation methods (AICc from ENMtools) require raw output.
As far as LPT, it sounds like you're talking about thresholds for reclassifying results into binary suitable/unsuitable coverages. Several different thresholds are provided with the Maxent html output (perhaps you mean minimum training presence?) that provide the values (cumulative or logistic) used to reclassify outputs in a GIS. Note these are not provided within the summary for replicated maxent models, only the individual runs. Hope that helps.