Welcome to CV. There are a number of confused statements in you question.
First: Your aim is not to "perform a statistically significant survey" as that isn't really a meaningful phrase. Your aim should be to test a hypothesis, or answer a research question, or estimate a parameter, or something like that.
Second, your whole second paragraph is problematic. It is unclear what it would mean for a group to be "significantly represented". You may mean that you want the mean (or median, or something) to be estimated to a certain precision.
Third, your third paragraph isn't wrong, but it's sort of backward. The usual way of looking at this would be to say "the smaller the sample, the higher the margin of error". As for how much can be justified, that's really up to you -- it is a substantive question, not a statistical one, and varies by field. For some cases (e.g. the size of a ball bearing) we may want a very, very precise estimate. For others, e.g. the amount of milk in a liter package, much less precision is needed.
The size of the population makes relatively little difference unless the sample size is a large proportion of the population. That may be the case here, as the population is pretty small. You can look up the "finite population correction".
Finally, to do a power analysis you need all but one of the following:
- Effect size you want to be able to detect and the test you will use to detect it
- Acceptable type 1 error
- Desired power
- Sample size
Then, for many tests, you can use a canned program such as GPower or PASS or the power functions in R, and so on, but for others, you many need to simulated data.
