Twitter ads are extremely expensive, wouldn't waste my time on it. Best way is to just produce high quality content and SEO the hell out of it.
It's actually not as bad as you think. I run follower campaigns only.
I am averaging 32 cents per follower, at 5$ per day using a 60 cent follower bid. My wordpress site makes more than that, so it's not really a true loss. My forum doesn't make any money at all (no ads yet), but the goal of it is actually to drive site engagement.
I used to run a lower bid, of 40 cents. It cost about 19 cents per follower, just got less per day.
In that, that costs an average of 3 cents over a 7 day period to push people to the site from twitter, per site conversion.
One way to keep the costs down is to run a retargeting/look-a-like campaign.
Target existing twitter followers that don't currently follow you, or their look-a-likes, or people who are similar to your already existing users.
Do I make money on that? No. Definitely not. It's a losing proposition, however I'm not so concerned about today's money, and more so concerned about tomorrow's viral growth. So long as the site makes more money than it costs (including paying authors), I really don't care about profits at this point.
Honestly, I'm in this more for the fun of it than profits.
My site is techraptor.net. We have close to 300 articles a month. "SEO the hell out of it" really isn't an option, since I can't get mostly volunteer (they don't get paid a whole lot) authors to write SEO perfect articles. It's also a news site, and one problem with news sites is that it takes some time to google index anything. (We do ping to make it faster, and run sitemaps)
By the time Google indexes it, it's no longer a hot topic
We have some basic SEO checks in place (automated tool has a checklist for them to meet), but it's like herding cats sometimes.