Given you have a good idea of where to start and are fairly confident you are speaking the same language as your client, jump start research by generating related keyphrases and long tail variants with the ever so easy to use Google Autocomplete. This tool makes predictions based on what you are typing that are a reflection of Google search activity.
This is another free tool for keyword research. The tool allows you to combine your keywords in a very easy manner. It has three main match types which include broad match, phrase match and the exact match. You can choose on any of them depending on your keyword search objectives. In addition, you can either use broad modifier or optional keyword or both. Most users are finding it to be a very useful tool in their search for the most appropriate keywords.
Search Analytics can be found under the 'Search Traffic' section and provides details of the keywords that drove clicks to your website, based on data for up to the last 90 days. The difference with Google's version is that you can filter the data to put extra context around the keywords, such as filtering by country to see keyword popularity based on country, which can be useful when carrying out keyword research for websites that service more than one country.
Jaaxy uses a combination of search engine data from the major search engines (Google, Bing and Yahoo) and Long Tail Pro get its search data from Google alone (via the Google Keyword Planner tool). While this seems to be an advantage for Jaaxy, you might only be interested in getting information from the number one search engine in the World: Google.
Long Tail Pro is a keyword research tool that helps you quickly find low competition keywords for your website. In particular, the tool is built for people doing SEO (search engine optimization) as opposed to people doing paid ads (Google Adwords PPC). I'm sure there are some advertisers that use the tool for paid ad keyword research, but the tool was built for SEO keyword research.