It's really not that much spam, twitters actually pretty clean and once you get your first account going it really gets a lot easier. I'll give you my formula then tell you some don'ts and how I see a lot of people doing it wrong. I'll use a social marketing blog example
1. Pick your blog niche and start growing.
Don't open up your twitter account with "Social Marketing Blog" - Who wants to follow that? Nobody! If you're trying to promote your social marketing blog start an account called "financial motivation" Or something of the sorts. You can post up pictures motivating people to be successful and all that, that'll grow great.
Really, when I used my personal account very frequently most of the niche accounts I followed were people that followed me or that one of my friends retweeted, and thats basically it. Follow right under 1k people per day, then unfollow anywhere from 500-2k in a single day. Separate these two actions as doing them in the same day tends to leads me to bans. I've had pretty good luck with unfollowing but they're a little more harsh about following
3. Like pictures
Don't spend a lot of time, following/posting works much better from personal experience. If you have a bot go for it, I have a couple imacros but I rarely use them, sometimes if I'm bored and I have a new account I'll let it run.
4. Post a lot
Gifs are great, usually get much more interaction from my experience. I wrote a script to steal year old tweets from the most popular account in my niches, I'll probably release it sometime.
5. Request user submissions in your posts if possible. Then tag the submitter in and they'll almost always repost, and maybe a few of his or her friends as well.
6. (Optional) - Switch the name of your twitter account to your brand.
I do this frequently, especially if I'm branding a product. But I also see myself leaving the original name and just promoting a blog/product separately quite often as well.
Repeat for a couple days, you should be at a couple thousand people in a couple days/weeks. It really varies on your niche. I just started a weed niche page and I'm already passed 700 followers in less then a week. Some niches grow much faster then others, especially with twitters younger user base.
DON'Ts - Take this list seriously
1. When someone follows you, don't tweet at them "Thanks for the follow @".
Seriously, this is like the biggest "don't follow this dude" red flag ever. It just screams I'm new to twitter and I don't really know what to do.
2. Don't use a lot of hashtags. Unlike networks like tumblr you should be very sparing about your hashtags in twitter. Many people will disagree but heres why.
When you see someone tweet and then leave 3 or 4 hashtags in the end it just makes the whole post unattractive and takes the aesthetics away from it. When someone works in your #keyword with the post, it normally fits well. Heres an example:
OKAY - "This #internetmarketing picture was too good not to share"
NOT OKAY - "This internet marketing picture was too good not to share #internetmarketing #funny #socialmedia #socialmarketing"
See what I mean? Just take my word on it if you're new to twitter.
One last added tip, when a topic is trending, tweet something funny about it especially if your page is growing. It'll bring you to a whole new audience and theres a much bigger chance of your tweet blowing up. If you have any questions I'd love to help.