The best websites are run by people who love them. If there's a subject you're passionate and knowledgeable about, making a site on that topic is a great way to go. If you're not interested in the subject of your site, it's going to show. It's going to be harder to get other sites to mention it or link to it, and your visitors will be unlikely to hang around long enough to buy a product or complete whatever action it is that makes you money. Ultimately, you should aim to create a unique site that fulfills a need that's currently under served or one that you can fulfill better than the competition. Another approach in crowded markets is to make a site with a unique angle that others aren't using. Whatever niche you choose, for long term viability you should focus on adding real value for your visitors.
Since your goal is to make money with your site, you also need to determine if there is a way to do that with the subject or niche you're considering. Making a one page site about what your cat likes to do during the day isn't likely to make you a penny. Making a site about pet products on the other hand could be very profitable. One good way to estimate the potential of a niche is through keyword research. This will tell you what keywords or phrases people use to search for your topic, how many searches there are, and how much people pay to advertise for those terms. Search isn't the only way you can get visitors, but it is one of the best. (We'll cover more ways to increase traffic to your site in our section on website promotion.) In any case, keyword research will tell you a lot about your niche.
The best tool to use for this research is Google's Adwords Keyword Tool***. There are three types of keyword/phrase volume numbers you'll be able to see with this tool: broad match, phrase match, and exact match. Broad match gives you the search volume for any phrase that contains the keywords you searched for within it, even if the word order is different. So if you're looking at "new york hotels" for example, "hotels in new york city" would be a match. Phrase match gives you the volume for any phrase that contains your phrase, but in the correct word order. If someone searched for "cheap new york hotels", that would be considered a phrase match. And exact match only shows numbers for searches that exactly match the phrase you typed. So the only exact match for "new york hotels" is "new york hotels".
Exact match numbers are a good initial indicator if you only rank for the exact phrase you're targeting. Phrase match is a good intermediate number. And broad match will give you an idea as to the potential of your site if it ranks for all terms associated with your main phrase, although it may include a significant amount of irrelevant traffic. We focus on exact match when doing our keyword research.
Aside from search volume in the Google Adwords Keyword Tool, you should add the column "Estimated Average CPC", which stands for the estimated average cost-per-click people who are adverting with Google Adwords pay each time someone clicks an ad after searching for a given term. If CPC is high, it's likely that there is good revenue potential in the term, otherwise advertisers wouldn't be paying high prices for each click. If CPC is very low, there's obviously less potential. However high traffic volume but low CPC terms can be as profitable as low traffic volume but high CPC terms. A good way to view the difference between various keyword/phrase potentials is to multiply the traffic volume by the CPC.
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***Note that Google's Keyword Tools, and all data Google shares with you, may be wildly incorrect. You may find the traffic volume for a given term is a small fraction of what Google suggests, or a multiple of it. Unfortunately this makes choosing the topic of your website much more difficult. But by looking at Google's numbers, comparing relative search volume for different terms with Google Trends, checking out the search results and the prevalence of other sites in the niche, and some common sense, you should at least have a place to start.