Deciding between chi square and t test
This is a very subtle question and I encourage you to read the Wikipedia articles on these different subjects (t-test, chi-squared test, p-value, etc) because the authors worked hard to combat common misconceptions about these commonly used statistical tests. Here is a rather oversimplified rule-of-thumb for these different tests:


t-test: Used when you are looking at the means of different populations. For example, you might want to determine whether the difference in the mean gene expression level between treated and untreated cells is different, or if the gene expression level of cells in a certain environment differs from what you would expect in a null hypothesis. Assumptions: You are assuming that the populations you are looking at are normally distributed. The variance of the populations is not known (that would be a Z-test), but it is assumed that the variance of each population is the same. Finally, for the t-test to work, the samples of the data from the two populations are assumed to be independent.
$\chi^2$ test: Several possibilities for this. The most common in biology is the Pearson $\chi^2$ test, which is used when you are looking at categorical data, like the number of pea plants with white or purple flowers and round or wrinkled seeds, and trying to see whether the number of individuals in each category is consistent with some null hypothesis (such as the number in each category you'd expect if the genes for flower color and seed shape are not linked). Assumptions: The data points were randomly and independently gathered from the population, and you have a reasonably large number of samples.


I'd hate to have made a huge mistake, so please edit my answer and/or contribute your own if you think I am completely misrepresenting these topics!