Why not get started right away with some free tools?
Perfect for examining trends over time, Google Trends lets you compare more than search term on the same plot. This is ideal when you've got ideas for different start points for your keyword phrases and you want to see which is most popular.
Moz Keyword Explorer
The Moz Keyword Explorer tool is free, but you're limited to 10 searches a month unless you want to upgrade to a paid account. That seems a fair way to do it, since with the free account you're getting to take good advantage of their excellent keyword planner tool.
Autocomplete with different search engines
Another way of finding out what is most popular is to start typing into the search bar of any search engine, and see what autocomplete suggests for you. Try it with Google, Bing, DuckDuckGo, and Yandex. You might notice different results in what autocomplete suggests on each search engine - this in itself is useful information.
Alexa site info
Alexa has a pretty impressive set of keyword information for millions of the most popular websites on the internet. The Alexa site info tool tells you keywords that bring visitors to the site, as well as keywords that they could be ranking for. The free version is accessible to anyone, no account needed. It displays only a small amount of the available data, but it's a pretty good indication of start points for keywords.
Even if your site does not yet have enough traffic to rank on the Alexa site info tool, it's very worthwhile to take a look at competitor sites this way.
Bing keyword research tool
With Bing being the default search engine for Microsoft browsers, it's well worth looking into the Bing keyword research tool. It's not just geared for advertisers, it's a keyword research tool geared toward webmasters. You'll need to sign in to access the tool.