What are some useful Twitter tools I should consider for my website?

Bryan, You ask about "Tools... for my Website" and then go on to say you are looking for ways to add followers and promote your B2B content site without spamming.
I see those as 2 different questions and the 3rd Q probably ought to be ‘what is a good “Dashboard” to use' to monitor your accounts.

1) ON Website 'tools' -
1A) On your Blog(s), articles, RSS feeds set them up with both a “FollowMe” and a "tweet this" snippet to make it easy for twitter users drawn to the site to tweet about your content. A full scale Share bar is even better.

1B) Consider embedding a twitter feed on your site. You may want to set up another or 'alternative' twitter account for different 'interests.' For Example: As I work in multiple businesses and Non-Profits (with other experts), I tweet selectively through separate twitter accounts for Branding @PropelYourBrand & @PropelBranding, for Sales: @PropellingSales & @SalesmenTrainer, for Promotional Marketing: @UMarketingUS, Non-Profit - @NonProfitSteve, etc.

1C) When you have developed a large or even a “reasonable” base of followers, I suggest that you add/embed a “TwitterCounter” to show off the size of your Following/Flock. You can see how that looks on a home page www.7ksm.com. Full disclosure it’s an organization I refer business to and work with from time-to-time; 7K Social Media.
- I believe those to be some of the most useful right now. There are others, its ever-changing.

2) For Tools to effectively add targeted/appropriate followers there are several out there. NOTE: Twitter Terms of service officially forbid the use of automation tools,

2A) The list building function within Twitter is pretty good. For List building I used to use TweepML, as they had an approved relationship with Twitter, but the interconnect was cut cut-off in November by a Twitter change and Agora/TweepML has yet to resurrect their service in a manner that meets Twitter's revised functionality and requirements. Many who were active on that are substituting Tweepie and now Tweepie has added functionality. I may add that too, and may not even bother to do my now 1x a month check-in on TweepML’s status.

2B) On the outside the box approach, using Tweetadder is currently one of those I see in many Social Media toolkits. It provides many ways to search twitter profiles and build lists to follow and request follow-backs on. You can create multiple standard Direct Messages, Replies, Thank You, etc... It has highly variable settings to appear as ‘human’ as possible.

SPAM / Not SPAM - Many people insert a shortened URL (e.g. tinyUrl) in their thanks and direct messages (that is built into Tweetadder and some other programs with an API link). Some call that “SPAM” others do not. Handled discretely with good reasoning it can be an effective tool. Typical messages I get from following people that I consider effective and not “SPAMMY”
“Thanks for following me, I tweet on “(CONTENT DESCRIPTION)” and you can also find my blog/LinkedIn Profile/FB Page at [URL]”. Lots of ways to cut down that to 140, don’t forget the # hashtag.

3) As to the Dashboard: I like the look of some and not others and that's a personal preference issue. Look at Tweetdeck, Hootsuite, SocialOmmph, and consider the "Rockmelt" browser. Those are some of the most widely used.

The above should give you a great start and if/when you are ready, I have more in depth thoughts and recommendations, and with the speed of new application introductions it an 'ever-changing' story.