For third party, we use Hootsuite. It allows us to monitor different lists we've set up but creating separate columns. When you follow a number of people it can be cumbersome to monitor the main feed.
It also allows us to research new followers, search keywords by location etc. Granted you can do all of this through Twitter directly, but we like the fact that we can track clicks, Google analytics and Facebook through one tool.
As with anything it's like going to a networking event, only online. Be genuine, provide value and don't focus strictly on sales. Like an earlier poster mentioned think of it as lead generation, not another broadcasting tool.