When creating a poll to judge the popularity of particular Congressional candidates, it's important first to determine which candidates will be part of the poll and which districts they represent. Knowing the boundaries of the district will keep the pollster from samplings outside of the requisite voting area.
Generally, the wider the net the pollster casts across the entire district and the greater number of voters sampled, the more accurate the poll will be. This includes sampling voters from different neighborhoods within the district, different ethnics groups, different age groups, different sexes, and different religions, among other factors. By oversampling, say, young Latinas, the pollster may get a very different reaction than if all sexes, ages, and ethnicities are sampled. Naturally, the makeup of the district will have an effect on whether certain groups are more heavily sampled than others.
Two primary sampling methods are commonly used. The first is called a "probability sample." In this method, every person in the defined population (in this case, the Congressional district) has an equal chance of being polled. One major advantage to probability sampling is that the pollster can fairly adequately determine how representative the polling sample correlates to the overall population. In other words, pollsters can determine accuracy within a certain margin of error.
The second method is called "non-probability sampling." In this method, the population sample a) does not give everyone an equal chance of being selected; b) is not selected randomly; and c) is not known to the pollster beforehand. Rather, participants are selected based on other means, such as volunteering, or "opting in," to the polling survey. Unfortunately, this method might wind up oversampling groups who are, for example, more politically active, and statistic models must be used to estimate margin of error, since there is no simple way to calculate it using this method.
Therefore, using a probability sample will typically give the most representative response of the population as a whole. Examples of probability samples include "random-digit dialing" (RDD) and "registration-based sampling" (RBS). The former involves calling all numbers with proper area codes and exchanges within the district, while the latter includes contacting registered voters culled from voter lists. RDD is more expensive, but it can often give a more accurate depiction of "likely" voters than the RBS system can.
Data from the polls commonly include a number of important data points, including a) the number of respondents polled; b) the total population they are meant to represent; c) the percentage of responses giving one candidate or another particular favorability ratings; and d) the margin of error showing how likely the polling group is to represent the population at large. Data could also be broken down into more specific sub-categories, such as age, race, religion, or sex.
Further Reading
You should recognize that the population from which you want to sample is not the residents of your district. Indeed, it is not the adult population, as not everyone is eligible to vote. Another restriction in many places is...
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the necessity of registering to vote.
So you might start with the registered voters in your district. You should also realize that many registered voters do not vote.
Your population ought to be likely registered voters—those voters who are registered in your district that have shown that they are likely to vote. (Note that this changes depending on the type and timing of elections: primary versus general elections and presidential versus non-presidential years. Also, there might be some local issue that drives extra voters to the polls or a lack of competition that depresses turnout.)
You should choose from a population of likely registered voters. Ideally, you would assign each voter a number and use a simple random sample. To help control expense, you might put the population in some order (geographical or alphabetical, for instance) and then select every fiftieth person. (Every nth person where n is decided to get the sample size you desire.) If you choose this type of sample, a systematic sample, you will want to start at a randomly chosen point. Another possibility is a cluster sample; select a random sample from each voting unit within your district. You would not want to use phone numbers, as many voters will not have landlines and some will not have any phone.
As long as the sample is large enough, it should be representative of the voting population. There are ways to enforce representation (weighting for factors such as age, sex, race, etc.) that can be used.
For your presentation of results, you might choose a bar graph with the contenders' names as the variable and the frequency percent as the vertical axis. (You will ultimately want to include error bounds in a confidence interval.)