I haven't worked with methylation data, but from what I understand, you should be applying limma on M-values. These are more accurately modelled under normality, at least in regard to the range of values, the mean-variance relationship, etc. Some people seem to do all the linear modelling with M-values, and then report back the fold-changes, etc. for significant probes in terms of beta-values, which are easier to interpret.
logFC field should represent the change in the average M-value between conditions, which - I think - is interpretable as a change in the log-odds of methylation. For example, a
logFC of 1 would indicate that in one condition, the odds of being methylated to being nonmethylated are twice as high as the other condition. Or, in the simplest terms: larger
logFC = stronger differential methylation. The
AveExpr field would be the average M-value across all samples, which gives you a measure of the overall amount of methylation for each probe. The B-statistic is the log-odds of differential methylation to constant methylation (note, not the log-odds of methylation to nonmethylation, which is the M-value itself). I tend not to use the B-statistic much for DE analyses as I find it a bit unintuitive, but to each his own.
Finally, the chosen reference depends on the parametrization of the design matrix. If you have a one-way layout and you construct a design with an intercept via
model.matrix, the alphabetically-first group will be the reference.