I would first apply Levene-test for checking if there are deviation of homogeneity of variances. Several test stats are robust against not to strong deviations from normal distribution of the data. If data are non-normal distributed or varianvces are not homogenious etc. why not transforming data? (e.g. square-root +0.5) There are many possibility depending on the form of the of data distribution.
Another possiblity is the use of multiple t-tests with bonferroni-holm adjustment of alpha error if I remember right.