There are several issues that only you can answer. 1) What is the level of accuracy that defines "reliable?" 2) What is the variability in the population being sampled? 3) What is the expected relationship and how do you define success? If half the patients die in the treatment and 52% die in the controls is this success? 4) What are the statistical methods you hope to use? 5) Are you sampling, or using a census? Alternatively, what is the population size? 6) Do you expect 100% participation, or is there a risk of failure for any given replicate? Failure may be non-responses in a survey, or losses when chemical plant #2 breaks down and takes 3 weeks to be repaired.

There are non-statistical considerations as well. 1) what is the cost per sample? 2) Are there ethical considerations in gathering the data? 3) Are there special risks? 4) Is this for publication? 5) What is your time frame? If you want to graduate next week, then you need to accept a very small sample size and whatever consequences thereof.

These are some of the issues that need to be considered when thinking about sample size.

You should play with a sample size calculator like G*Power. http://gpower.hhu.de/

However, sample size calculators give you a lower bound to your sample size that is only as accurate as the numbers you supply to the calculator. The answer is dependent on the types of statistical tests. If your methodology does not fit the sample size calculator then you could try simulation. If you have to pick a number and hope for the best then something between 30 and 500 per treatment is a fair guess, subject to issues of reliability. Also subject to your goals. If you are trying to estimate the likelihood of some rare event, then 500,000,000 may not be sufficient.

Example: So I study the movement of Huanglongbing disease of citrus. The disease is vectored by an insect. If I am growing citrus in Australia, I might want to prove that Australia is disease free. Well, there are many millions of psyllids that could vector the disease, and I cannot capture all of them. So I make a political statement that Australia is disease free so long as I do not capture a diseased insect. I test 10 psyllids each month and none test positive for the disease. If the probability of capturing an infected insect is 0.0000000001, then I will likely miss the initial stages of the disease with this sample size. I need about 2 orders of magnitude more samples than the inverse of the infection rate to have a reliable chance of even detecting the event (about 1E12 insects in this case).

It was a good question, but it is one that only you can answer. Based on the current state of knowledge it is possible that you will have to guess and hope for the best. In that case I would collect as much data as possible given the available time/budget. I would read journal articles to see what is generally considered publishable. If your time/budget constraints do not allow you to reach a publishable level then I would consider a different project that fits within your constraints. At a minimum, your advisor must approve the sample size. There is usually no problem exceeding that if you want to make the study better, but having a smaller sample size risks trouble.