Power Analysis - Determining Sample Size for Many Data Categories

I'm conducting an experiment in which people from three different cultural backgrounds are placed in different social contexts (for example, needing to ask for help). In each context they must write a dialogue, or mock e-mail. I'll analyze their politeness strategies which I count to be about 30 different types, seeing how their choices differ across cultures.

My biggest problem is, naturally, how to set this all up. I'm guessing I should think of the first cultural background as a group and first consider politeness strategy A, treating it like a 0-1 box. A 0 means any other strategy was used and a 1 means A was used. Then do the same for strategy B: 0 means anything else was used, 1 means B was used. Then do this with each of the other cultural groups. This seems painfully laborious but perhaps it's what must be. Is there an easier, more natural way?

If this were my technique, then I would perform a two-tailed test in which the null hypothesis is that the averages over cultures are equal, and compare each with respect to each strategy. I need to know how many participants are required for meaningful results, given a .05 significance level and a .8 power. I'm not exactly sure what my effect size should be, but I think .8 sounds pretty strong--maybe I should just go with .5? I also don't know what my expected mean or standard deviation should be. I'm also not totally sure how to input these calculations into G*Power. Particularly, it asks whether I want an exact calculation, t-test, F-test, chi^2-test, or z-test. Pretty sure, because I'm looking at a sample of a population I want a t-test. Under t-test it offers various types of tests: Correlation, linear regression, means, and generic t-test. Because I'm setting it up as calculating means, this seems the natural choice. Under means it gives the options, two independent groups, two dependent groups, and then some options that start with the name Wilcoxon. Could anyone help me understand the differences between all of these options?