Theres a few other things you should take into consideration with Twitter.
A retweet from someone from little to no followers is kinda useless. It also makes me wonder if they are a spam bot. It won't nessecarly generate any good will.
I have a couple of Twitter accounts. 1 business. I use the business account to provide product updates, downtime notifications etc
2. personal. My personal account is based around music and a personal blog/brand I have built over many years in a very small niche. Through this I have achieved a decent amount of followers that I interact with reguarly. I have also been able to convert a good portion of followers. My followers have also recommend my services to their followers knowing that I offer the service their contact is looking for. Even when they don't use my services. It makes them look like an authority/knowledgable person with contacts.
I saw a tweet that made sense. It was something like "facebook is for friends that you hate, twitter is for people you don't know but love". This is true. My twitter feed is not disimilar to an active forum.
My best advice is:
Create a personal account, build followers in your niche by interacting with them (even if at first they don't respond)
Be real. Sounds cliche but, twitter is about interaction, communicating and sharing thoughts with similar minded people... And you better believe they will all be similar minded. During recent elections here in Australia, it seemed everyone was giving their 2 cents about how Labour should win. If the election was based off my feed, they would have won. They didn't and we now have a new Prime Minister.
Be careful with the links you provide. Especially early on while people are getting to know you. If you over do it, an unfollow is only a click away.
In all honesty, if you are new to Twitter and want to promote your company, I would use their paid ads. Why ? Because you can define the audience you are trying to attract. At first I detested twitter ads, but since they';ve fine tuned it, I do often click a link or at least favourite it so I can come back and look at it later. In saying that, make sure your site is responsive. Damn, I hate clicking a twitter link to find it's not working on my browser.
Smartcompany.com.au were guilty of this and it annoyed the shit out of me as they have really interesting headers. i.e. I'd click through and would get page not found.
Don't tweet people/companies with a link to your site. If it's a new account and you do this reguarly you're looking at a ban. Users hate this. Trying to get followers by favouriting their tweets in the hope of a followback, is also a no no.
I think AJ Ghergich @seo has found a really good balance for Twitter. He posts a lot of great links to other people sites, many sites I haven't seen before and he interacts with his followers. @randfish is also Ok. Though he doesn't interact unless you're a seo celebrity or similar.
I guess the same rings true for twitter as it does for SEO. Look for authorities who are active and interesting.
Hope that helps