Be very careful of getting followers. I know you want to extend your reach. But I can tell you from experience that once you get over 1000, the idiots start to notice you. You’re not likely to be suspended or deleted if under 1000. Plus after 1000, it’s hard to keep up with the new follows and likes and comments. You’re a nice person and probably want to make sure every comment is at least read.
Now, when you get over 5000 that’s when the bots and morons really like to notice you. You spend a lot of time blocking and muting and such. Empty work because your twit ain’t making no money. Amiright?
That said, if you want followers the best thing you can do is simply ask publicly. Second is to jump on some trains. And third is to comment in the big accounts with supporting/debunking information backed up by SAUCE. “I heard this” or “I heard that” will get you ignored. Also, when commenting on the big accounts try to get in early on the conversation. The earlier the better to get noticed. This is the most organic way and your followers likely do so based on merit.
Lastly, and in the meritorious spirit, have good content on your line. Raw re-tweets or re-tweets with short comments will not get you followers. You gotta have something original to gain a following. That shouldn’t be a problem for you. If you can get a re-tweet from a big account you’ll get a lot of instant followers.
Personally I’m not trying to get new followers, but I do follow back anyone who follows me. That common courtesy goes a long way. Being nice certainly helps.